ALBERT

All Library Books, journals and Electronic Records Telegrafenberg

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
Filter
  • Articles  (58)
  • 17B37  (58)
  • 1990-1994  (58)
  • Mathematics  (58)
Collection
  • Articles  (58)
Source
Keywords
Publisher
Years
Year
Topic
  • 1
    Electronic Resource
    Electronic Resource
    Quantum homogeneous spaces, duality and quantum 2-spheres (1994)
    Springer
    Geometriae dedicata 52 (1994), S. 291-315 
    Details
    ISSN: 1572-9168
    Keywords: 16W30 ; 17B37 ; 22E99 ; quantum groups ; quantum homogeneous spaces ; coaction ; dual Hopf algebras ; two-sided coideals ; infinitesimal invariance ; quantum SU(2) ; sl(2) quantized universal enveloping algebra ; quantum 2-spheres
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For a quantum groupG the notion of quantum homogeneousG-space is defined. Two methods to construct such spaces are discussed. The first one makes use of quantum subgroups, the second more general one is based upon the notion of infinitesimal invariance with respect to certain two-sided coideals in the Hopf algebra dual to the Hopf algebra ofG. These methods are applied to the quantum group SU(2). As two-sided coideals we take the subspaces spanned by twisted primitive elements in the sl(2) quantized universal enveloping algebra. A one-parameter series of mutually non-isomorphic quantum 2-spheres is obtained, together with the spectral decomposition of the corresponding right regular representation of quantum SU(2). The link with the quantum spheres defined by Podleś is established.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01278478
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    An elliptic quantum algebra for $$\widehat{s1}_2 $$ 2 (1994)
    Springer
    Letters in mathematical physics 32 (1994), S. 259-268 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 82A67
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract An elliptic deformation of $$\widehat{s1}_2 $$ is proposed. Our presentation of the algebra is based on the relationRLL = LLR *, whereR andR * are eight-vertexR-matrices with the elliptic moduli chosen differently. In the trigonometric limit, this algebra reduces to a quotient of that proposed by Reshetikhin and Semenov-Tian-Shansky. Conjectures concerning highest-weight modules and vertex operators are formulated, and the physical interpretation ofR * is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00750668
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    On affine yangians (1994)
    Springer
    Letters in mathematical physics 32 (1994), S. 269-274 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 81R50 ; 82B23
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A Yangian $$Y(\widetilde{sl}(2))$$ , a deformation of the universal enveloping algebra of the two-dimensional loop algebra sl(2) ⊗C [t −1,t;u], is constructed. This deformation is an analogue of a Yangian which was constructed by V. Drinfeld for any simple Lie algebra. The PBW theorem for $$Y(\widetilde{sl}(2))$$ is proved and some representations are constructed. Like usual Yangians, $$Y(\widetilde{sl}(2))$$ possesses a one-dimensional group of auto- morphisms and at zero level - a two-dimensional group of automorphisms. This observation allows one to conjecture that the representation theory of $$Y(\widetilde{sl}(2))$$ should give rise to new solutions of QYBE. Yangians of other affine algebras can be constructed similarly and they enjoy similar properties.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00761137
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    Heisenberg realization for U q (sl n ) on the flag manifold (1994)
    Springer
    Letters in mathematical physics 30 (1994), S. 35-43 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 16S32 ; 81R10 ; 33D80
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We give the Heisenberg realization for the quantum algebra U q (sl n ), which is written by theq-difference operator on the flag manifold. We construct it from the action of U q (sl n ) on theq-symmetric algebraA q (Mat n ) by the Borel-Weil-like approach. Our realization is applicable to the construction of the free field realization for U q $$(\widehat{s1_n })$$ [2].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00761420
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    Electronic Resource
    Electronic Resource
    Small representations of quantum affine algebras (1994)
    Springer
    Letters in mathematical physics 30 (1994), S. 131-145 
    Details
    ISSN: 1573-0530
    Keywords: 17B37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We characterize the finite-dimensional representations of the quantum affine algebra U q ( $$\widehat{sl}$$ n+1) (whereq ∈ ℂ× is not a root of unity) which are irreducible as representations of U q (sl n+1). We call such representations ‘small’. In 1986, Jimbo defined a family of homomorphismsev a from U q (sl n+1) to (an enlargement of) U q (sl,n+1), depending on a parametera ∈ ℂ·. A second family,ev a can be obtained by a small modification of Jimbo's formulas. We show that every small representation of U q ( $$\widehat{sl}$$ n+1) is obtained by pulling back an irreducible representation of U q (sl n+1) byev a orev a for somea ∈ ℂ·.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939701
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 6
    Electronic Resource
    Electronic Resource
    Free boson representation of $$U_q (\widehat{sl}_3 )$$ (1994)
    Springer
    Letters in mathematical physics 30 (1994), S. 207-216 
    Details
    ISSN: 1573-0530
    Keywords: 81R50 ; 16W30 ; 17B37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A representation of the quantum affine algebra $$U_q (\widehat{sl}_3 )$$ of an arbitrary levelk is constructed in the Fock module of eight boson fields. This realization reduces the Wakimoto representation in theq → 1 limit. The analogues of the screening currents are also obtained. They commute with the action of $$U_q (\widehat{sl}_3 )$$ modulo total differences of some fields.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00805853
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 7
    Electronic Resource
    Electronic Resource
    Algebraic deformation program on minimal nilpotent orbit (1994)
    Springer
    Letters in mathematical physics 30 (1994), S. 241-250 
    Details
    ISSN: 1573-0530
    Keywords: 17B35 ; 17B37 ; 22E46
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We construct an algebraic star product on the minimal nilpotent coadjoint orbit of a simple complex Lie group with a Lie algebra which is not of typeA n. According to the deformation program, we study the representations of the Lie algebra associated to this orbit.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00805856
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 8
    Electronic Resource
    Electronic Resource
    Quantized affine Lie algebras and diagonalization of braid generators (1994)
    Springer
    Letters in mathematical physics 30 (1994), S. 267-277 
    Details
    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Let U q $$(\hat{\mathcal{G}})$$ be a quantized affine Lie algebra. It is proven that the universal R-matrix R of U q $$(\hat{\mathcal{G}})$$ satisfies the celebrated conjugation relationR + =TR withT the usual twist map. As applications, the braid generator is shown to be diagonalizable on arbitrary tensor product modules of integrable irreducible highest weight U q $$(\hat{\mathcal{G}})$$ -module and a spectral decomposition formula for the braid generator is obtained which is the generalization of Reshetikhin and Gould forms to the present affine case. Casimir invariants are constructed and their eigenvalues computed by means of the spectral decomposition formula. As a by-product, an interesting identity is found.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00751063
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 9
    Electronic Resource
    Electronic Resource
    On aq-deformation of the discrete Painlevé I equation andq-orthogonal polynomials (1994)
    Springer
    Letters in mathematical physics 30 (1994), S. 327-336 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 33D45 ; 39A70 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We present aq-analog of the discrete Painlevé I equation, and a special realization of it in terms ofq-orthogonal polynomials.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00751068
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 10
    Electronic Resource
    Electronic Resource
    Metric on quantum spaces (1994)
    Springer
    Letters in mathematical physics 31 (1994), S. 35-39 
    Details
    ISSN: 1573-0530
    Keywords: 46L87 ; 81R50 ; 17B37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We introduce the analogue of the metric tensor in the case ofq-deformed differential calculus. We analyse the consequences of the existence of the metric, showing that this enforces severe restrictions on the parameters of the theory. We discuss in detail examples of the Manin plane and theq-deformation of SU(2). Finally we touch the topic of relations with Connes' approach.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00751169
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 11
    Electronic Resource
    Electronic Resource
    Casimir invariants for quantized affine Lie algebras (1994)
    Springer
    Letters in mathematical physics 31 (1994), S. 77-83 
    Details
    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Casimir invariants for quantized affine Lie algebras are constructed and their eigenvalues computed in any irreducible highest-weight representation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00751173
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 12
    Electronic Resource
    Electronic Resource
    Quantum affine algebras and universalR-matrix with spectral parameter (1994)
    Springer
    Letters in mathematical physics 31 (1994), S. 101-110 
    Details
    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Using the previously obtained universalR-matrix for the quantized nontwisted affine Lie algebras U q (A 1 (1) ) and U q (A 2 (1) ), we determine the explicitly spectral dependent universalR-matrix for the corresponding quantum Lie algebras U q (A 1) and U q (A 2). As applications, we reproduce the well known results in the fundamental representations and we also derive an extremely explicit formula of the spectral-dependentR-matrix for the adjoint representation of U q (A 2), the simplest nontrivial case when the tensor product decomposition of the representation with itself has nontrivial multiplicity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00750144
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 13
    Electronic Resource
    Electronic Resource
    Quantization of U q [so(2n + 1)] with deformed para-Fermi operators (1994)
    Springer
    Letters in mathematical physics 31 (1994), S. 151-157 
    Details
    ISSN: 1573-0530
    Keywords: 81R50 ; 16W30 ; 17B37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The observation thatn pairs of para-Fermi (pF) operators generate the universal enveloping algebra of the orthogonal Lie algebra so(2n + 1) is used in order to define deformed pF operators. It is shown that these operators are an alternative to the Chevalley generators. With this background U q [so(2n + 1)] and its ‘Cartan-Weyl’ generators are written down entirely in terms of deformed para-Fermi operators.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00750149
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 14
    Electronic Resource
    Electronic Resource
    R-matrix method for Heisenberg quantum groups (1994)
    Springer
    Letters in mathematical physics 31 (1994), S. 159-166 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 81R50 ; 70H05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract TheR-matrix method is systematically applied to get several Heisenberg quantum groups depending on two or three parameters. It turns out that the associatedR-matrices have to verify a weaker form of the QYBE. Only for particular cases of quantum groups, we can imposeR to be a solution of the QYBE. The corresponding quantum Heisenberg Lie algebras are obtained by duality.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00750150
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 15
    Electronic Resource
    Electronic Resource
    Poisson structures on the Lorentz group (1994)
    Springer
    Letters in mathematical physics 32 (1994), S. 11-23 
    Details
    ISSN: 1573-0530
    Keywords: 22E46 ; 17B37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Poisson-Lie structures on the Lorentz group are completely classified. A method applicable to an arbitrary semisimple complex Lie group (treated as real) is developed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00761120
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 16
    Electronic Resource
    Electronic Resource
    Classification of three-dimensional covariant differential calculi on Podles' quantum spheres and on related spaces (1994)
    Springer
    Letters in mathematical physics 32 (1994), S. 25-36 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 46L87 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Covariant differential calculi on the quantum space $$\mathfrak{X}_{q\lambda \rho }$$ for the quantum group SL q (2) are classified. Our main assumptions are thatq is not a root of unity and that the differentials de j of the generators of $$\mathfrak{X}_{q\lambda \rho }$$ form a free right module basis for the first-order forms. Our result says, in particular, that apart from the two casesc =c(3), ∞ there exists a unique differential calculus with the above properties on the space $$\mathfrak{X}_{q\lambda \rho }$$ which corresponds to Podles' quantum sphereS qc /2 .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00761121
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 17
    Electronic Resource
    Electronic Resource
    Representation theory of quantized poincaré algebra. tensor operators and their applications to one-particle systems (1994)
    Springer
    Letters in mathematical physics 32 (1994), S. 85-101 
    Details
    ISSN: 1573-0530
    Keywords: 81R50 ; 16W30 ; 17B37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A representation theory of the quantized Poincaré (κ-Poincaré) algebra (QPA) is developed. We show that the representations of this algebra are closely connected with the representations of the nondeformed Poincaré algebra. A theory of tensor operators for QPA is considered in detail. Necessary and sufficient conditions are found in order for scalars to be invariants. Covariant components of the four-momenta and the Pauli-Lubanski vector are explicitly constructed. These results are used for the construction of someq-relativistic equations. The Wigner-Eckart theorem for QPA is proven.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00739419
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 18
    Electronic Resource
    Electronic Resource
    Diagonalization of the braid generator on unitary irreps of quantum supergroups (1994)
    Springer
    Letters in mathematical physics 32 (1994), S. 231-240 
    Details
    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is shown that the braid generator σ associated with the universalR-matrix is diagonalizable on all unitary representations of quantum supergroups. An example is considered using U q (gl(2|1)) and a family of eight-dimensional typical representations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00750665
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 19
    Electronic Resource
    Electronic Resource
    Left regular representation and contraction of sl q (2) to e q (2) (1994)
    Springer
    Letters in mathematical physics 32 (1994), S. 249-258 
    Details
    ISSN: 1573-0530
    Keywords: 16W30 ; 17B37 ; 81R10 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The left regular representation of the quantum algebras sl q (2) and e q (2) are discussed and shown to be related by contraction. The reducibility is studied andq-difference intertwining operators are constructed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00750667
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 20
    Electronic Resource
    Electronic Resource
    Simple WZW superselection sectors (1993)
    Springer
    Letters in mathematical physics 28 (1993), S. 31-41 
    Details
    ISSN: 1573-0530
    Keywords: 16W30 ; 17B37 ; 81T05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The superselection structure of simple currents of chiral Wess-Zumino-Witten theories, at arbitrary valuek ∈ ℕ of the corresponding affine Lie algebra, is described in terms of explicit localizable automorphisms of the affine algebra. These automorphisms are induced by certain Dynkin diagram automorphisms; under composition, they form an Abelian group isomorphic to the center of the relevant simply connected simple Lie group and, hence, reproduce the WZW fusion rules.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00739564
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 21
    Electronic Resource
    Electronic Resource
    Stochastic differential calculus, the Moyal *-product, and noncommutative geometry (1993)
    Springer
    Letters in mathematical physics 28 (1993), S. 123-137 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 58A10 ; 58G32 ; 81R50 ; 81S20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A reformulation of the Itô calculus of stochastic differentials is presented in terms of a differential calculus in the sense of noncommutative geometry (with an exterior derivative operator d satisfying d2 = 0 and the Leibniz rule). In this calculus, differentials do not commute with functions. The relation between both types of differential calculi is mediated by a generalized Moyal *-product. In contrast to the Itô calculus, the new framework naturally incorporates analogues of higher-order differential forms. A first step is made towards an understanding of their stochastic meaning.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00750305
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 22
    Electronic Resource
    Electronic Resource
    The double of a Jacobian quasi-bialgebra (1993)
    Springer
    Letters in mathematical physics 28 (1993), S. 13-29 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 16W30 ; 17B70
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We show that the construction of the double of a Lie bialgebra can be extended to the case where a vector space is only equipped with the structure of a Jacobian quasi-bialgebra (also called a Lie quasi-bialgebra). In this case, the double is itself a Jacobian quasi-bialgebra and it is quasi-triangular. The more general case of the double of a proto-Lie bialgebra is also discussed. In the first section, the notions of exact, strictly exact, quasi-triangular and triangular Jacobian quasi-bialgebras are defined and their equivalence classes under twisting are studied.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00739563
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 23
    Electronic Resource
    Electronic Resource
    Representations of the coordinate ring of GL q (3) (1993)
    Springer
    Letters in mathematical physics 28 (1993), S. 207-217 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is shown that finite-dimensional irreducible representations of the quantum matrix algebraM q (3) (the coordinate ring of GL q (3)) exist only whenq is a root of unity (q p = 1). The dimensions of these representations can only be one of the following values:p 3,p 3/2,p 3/4, orp 3/8. The topology of the space of states ranges between two extremes, from a three-dimensional torusS 1 ×S 1 ×S 1 (which may be thought of as a generalization of the cyclic representation) to a three-dimensional cube [0, 1] × [0, 1] × [0, 1].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00745152
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 24
    Electronic Resource
    Electronic Resource
    On PBW bases for Yangians (1993)
    Springer
    Letters in mathematical physics 27 (1993), S. 37-42 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 81R50 ; 82B23
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract PBW bases for Yangians are constructed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00739587
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 25
    Electronic Resource
    Electronic Resource
    Baxterization of ther-matrix for the adjoint representation of U q [D(2, 1;α)] (1993)
    Springer
    Letters in mathematical physics 27 (1993), S. 51-58 
    Details
    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The Baxterization procedure is applied to the Braid group representation arising from the adjoint representation of the quantum supergroup U q [D(2, 1;α)]. This yields a two-parameter family of solutions to the (parameter dependent) Yang-Baxter equation of interest in supersymmetric lattice models.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00739589
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 26
    Electronic Resource
    Electronic Resource
    On the quantum group and quantum algebra approach toq-special functions (1993)
    Springer
    Letters in mathematical physics 27 (1993), S. 179-190 
    Details
    ISSN: 1573-0530
    Keywords: 22E70 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Two interpretations ofq-special functions based on quantum groups and algebras have been presented in the literature. The connection between these approaches is explained using as an example the case whereU q (sl(2)) is the basic structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00739576
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 27
    Electronic Resource
    Electronic Resource
    Boson realizations of quantum algebras and some physical spaces with quantum algebra symmetry (1993)
    Springer
    Letters in mathematical physics 27 (1993), S. 273-277 
    Details
    ISSN: 1573-0530
    Keywords: 81R50 ; 17B37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The generators ofq-boson algebra are expressed in terms of those of boson algebra, and the relations among the representations of a quantum algebra onq-Fock space, on Fock space, and on coherent state space are discussed in a general way. Two examples are also given to present concrete physical spaces with quantum algebra symmetry. Finally, a new homomorphic mapping from a Lie algebra to boson algebra is presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00777374
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 28
    Electronic Resource
    Electronic Resource
    On spectral properties ofq-oscillator operators (1993)
    Springer
    Letters in mathematical physics 29 (1993), S. 13-18 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 33D25 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The property of self-adjointness of the operatorQ =a + +a - in three types ofq-oscillator algebras is considered. Spectral measures and generalized eigenfunctions ofQ are found in the cases when this operator is bounded. Generalized eigenvectors are expressed in terms ofq-Hermite polynomials. If the operatorQ is unbounded, then its closure $$\bar Q$$ is not self-adjoint. However, in this case, $$\bar Q$$ admits self-adjoint extensions. Deficiency subspaces are one-dimensional. These subspaces are explicitly found.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00760854
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 29
    Electronic Resource
    Electronic Resource
    On universalR-matrix for quantized nontwisted rank 3 affine KM algebras (1993)
    Springer
    Letters in mathematical physics 29 (1993), S. 19-31 
    Details
    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Explicit formulas of the universalR-matrix are given for all quantized nontwisted rank 3 affine KM algebras U q (A 2 (1) ), U q (C 2 (1) ) and U q (G 2 (1) ).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00760855
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 30
    Electronic Resource
    Electronic Resource
    Difference schrödinger operators with linear and exponential discrete spectra (1993)
    Springer
    Letters in mathematical physics 29 (1993), S. 63-73 
    Details
    ISSN: 1573-0530
    Keywords: 33D45 ; 39A70 ; 17B37 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Using the factorization method, we construct finite-difference Schrödinger operators (Jacobi matrices) whose discrete spectra are composed from independent arithmetic, or geometric series. Such systems originate from the periodic, orq-periodic closure of a chain of corresponding Darboux transformations. The Charlier, Krawtchouk, Meixner orthogonal polynomials, theirq-analogs, and some other classical polynomials appear as the simplest examples forN = 1 andN = 2 (N is the period of closure). A natural generalization involves discrete versions of the Painlevé transcendents.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00760860
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 31
    Electronic Resource
    Electronic Resource
    Fusion structures from quantum groups: II. Why truncation is necessary (1993)
    Springer
    Letters in mathematical physics 29 (1993), S. 83-90 
    Details
    ISSN: 1573-0530
    Keywords: 16W30 ; 17B37 ; 81R50 ; 81T05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is shown that a finite, reflection positive, and nontruncated fusion structure on an arbitrary Hopf algebraℋ is trivial in the sense thatq-traces coincide with ordinary traces andq-dimensions coincide with ordinary dimensions. Thus, nontruncated fusion structures are ruled out to describe the fusion rules of quantum field theories with noninteger statistical dimensions and a finite number of superselection sectors.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00749724
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 32
    Electronic Resource
    Electronic Resource
    On quantum multi-hamiltonian systems (1993)
    Springer
    Letters in mathematical physics 29 (1993), S. 197-203 
    Details
    ISSN: 1573-0530
    Keywords: 81R50 ; 81B05 ; 17B37 ; 70H05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract On studying various examples with one degree of freedom, we discuss the possibility of extending the classical concept of multi-Hamiltonian systems to the quantum domain. We show that an adaptation is possible in each case generally leading to distinguish classes of systems characterized globally by their observable algebras.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00761107
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 33
    Electronic Resource
    Electronic Resource
    Duality for a Lorentz quantum group (1993)
    Springer
    Letters in mathematical physics 29 (1993), S. 259-269 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 16W30 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We give the algebra ℒ q /* dual to the matrix Lorentz quantum group ℒ q of Podles-Woronowicz, and Watamuraet al. As a commutation algebra, it has the classical form ℒ q /* ≅ U q (sl(2, ℂ)) ⊗ U q (sl(2, ℂ)). However, this splitting is not preserved by the coalgebra structure which we also give. For the derivation, we use a generalization of the approach of Sudbery, viz. tangent vectors at the identity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00750960
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 34
    Electronic Resource
    Electronic Resource
    On a possible algebra morphism of U q [osp(1/2n)] onto the deformed oscillator algebra W q (n) (1993)
    Springer
    Letters in mathematical physics 28 (1993), S. 187-193 
    Details
    ISSN: 1573-0530
    Keywords: 81R50 ; 16W30 ; 17B37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We formulate a conjecture stating that the algebra ofn pairs of deformed Bose creation and annihilation operators is a factor algebra of U q [osp(1/2n)], considered as a Hopf algebra, and prove it for then = 2 case. To this end, we show that for any value ofq, U q [osp(1/4)] can be viewed as a superalgebra freely generated by two pairsB 1 ± ,B 2 ± of deformed para-Bose operators. We write down all Hopf algebra relations, an analogue of the Cartan-Weyl basis, the ‘commutation’ relations between the generators and a basis in U q [osp(1/2n)] entirely in terms ofB 1 ± ,B 2 ± .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00745150
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 35
    Electronic Resource
    Electronic Resource
    Self-similar potentials and theq-oscillator algebra at roots of unity (1993)
    Springer
    Letters in mathematical physics 28 (1993), S. 59-74 
    Details
    ISSN: 1573-0530
    Keywords: 34L40 ; 17B37 ; 33D80 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Properties of the simplest class of self-similar potentials are analyzed. Wave functions of the corresponding Schrödinger equation provide bases of representations of theq-deformed Heisenberg-Weyl algebra. When the parameterq is a root of unity, the functional form of the potentials can be found explicitly. The generalq 3 = 1 and the particularq 4 = 1 potentials are given by the equi-anharmonic and (pseudo) lemniscatic Weierstrass functions, respectively.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00739567
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 36
    Electronic Resource
    Electronic Resource
    A superalgebra morphism of U q [osp(1/2N)] onto the deformed oscillator superalgebra W q (N) (1993)
    Springer
    Letters in mathematical physics 28 (1993), S. 321-328 
    Details
    ISSN: 1573-0530
    Keywords: 81R50 ; 16W30 ; 17B37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We prove that the deformed oscillator superalgebra W q (n) (which in the Fock representation is generated essentially byn pairs ofq-bosons) is a factor algebra of the quantized universal enveloping algebra U q [osp(1/2n)]. We write down aq-analog of the Cartan-Weyl basis for the deformed osp(1/2n) and also give an oscillator realization of all Cartan-Weyl generators.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00761500
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 37
    Electronic Resource
    Electronic Resource
    Primitive ideals of C q [SL(3)] (1993)
    Springer
    Communications in mathematical physics 156 (1993), S. 581-605 
    Details
    ISSN: 1432-0916
    Keywords: Quantum group ; primitive ideal ; Poisson Lie group ; symplectic leaves ; 17B37 ; 16W30 ; 16S80 ; 16S30 ; 58F06 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The primitive ideals of the Hopf algebraC q [SL(3)] are classified. In particular it is shown that the orbits in PrimC q [SL(3)] under the action of the representation groupH ≅C *×C * are parameterized naturally byW×W, whereW is the associated Weyl group. It is shown that there is a natural one-to-one correspondence between primitive ideals ofC q [SL(3)] and symplectic leaves of the associated Poisson algebraic groupSL(3,C).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02096864
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 38
    Electronic Resource
    Electronic Resource
    Closed star products and cyclic cohomology (1992)
    Springer
    Letters in mathematical physics 24 (1992), S. 1-12 
    Details
    ISSN: 1573-0530
    Keywords: 19P55 ; 17B37 ; 81S30 ; 19K56
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We define the notion of a closed star product. A (generalized) star product (deformation of the associative product of functions on a symplectic manifold W) is closed iff integration over W is a trace on the deformed algebra. We show that for these products the cyclic cohomology replaces the Hochschild cohomology in usual star products. We then define the character of a closed star product as the cohomology class (in the cyclic bicomplex) of a well-defined cocycle, and show that, in the case of pseudodifferential operators (standard ordering on the cotangent bundle to a compact Riemannian manifold), the character is defined and given by the Todd class, while in general it fails to satisfy the integrality condition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00429997
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 39
    Electronic Resource
    Electronic Resource
    Quantum groups and diagonalization of the braid generator (1992)
    Springer
    Letters in mathematical physics 24 (1992), S. 183-196 
    Details
    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is shown that the braid generator is diagonalizable on arbitrary tensor product modules V ⊗ V, V an irreducible module for a quantum group. A generalization of the Reshetikhin form for the braid generator is thereby obtained in the general case. As an application, a general closed formula is determined for link polynomials.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00402893
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 40
    Electronic Resource
    Electronic Resource
    Serre-type relations for special linear Lie superalgebras (1992)
    Springer
    Letters in mathematical physics 24 (1992), S. 173-181 
    Details
    ISSN: 1573-0530
    Keywords: 17A70 ; 16W30 ; 17B37 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is pointed out that, for m, n ≥2, the naive Serre presentation corresponding to the simplest Cartan matrix of sl(m, n) does not define the Lie superalgebra sl(m, n) but a larger algebra s(m, n) of which sl(m, n) is a nontrivial quotient. The supplementary relations for the generators are found and the definition of the q-deformed universal enveloping algebra of sl(m, n) is modified accordingly.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00402892
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 41
    Electronic Resource
    Electronic Resource
    Construction of a new quantum double and new solutions to the Yang-Baxter equation (1992)
    Springer
    Letters in mathematical physics 24 (1992), S. 197-203 
    Details
    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A new quantum double is established from a new Hopf algebra and a new kind of quantum R-matrix is obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00402894
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 42
    Electronic Resource
    Electronic Resource
    Real forms of U q(g) (1992)
    Springer
    Letters in mathematical physics 24 (1992), S. 49-58 
    Details
    ISSN: 1573-0530
    Keywords: 16W30 ; 57T05 ; 17B37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract In this Letter we consider the real forms of quantum groups associated to generalized Cartan matrices. There are two main results. The first is a description of the Hopf algebra automorphisms and of the Hopf *-algebra structures of the quantum group. This immediately yields a precise description of the real forms. The second result establishes a correspondence of these real forms when the quantum group is associated to a complex simple Lie algebra with objects associated to the real forms of the classical object.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00430002
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 43
    Electronic Resource
    Electronic Resource
    The uniqueness theorem for the universal R-matrix (1992)
    Springer
    Letters in mathematical physics 24 (1992), S. 231-244 
    Details
    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Up to now, the universal R-matrix for quantized Kac-Moody algebras Here the name \lsKac-Moody algebras\rs includes all semisimple finite-dimensional Lie algebras and all infinite-dimensional affine Kac-Moody algebras. is believed to be uniquely determined (for some ansatz) by properties of a quasi-cocommutativity and a quasi-triangularity. We prove here that the universal R-matrix (for the same ansatz) is uniquely determined by the property of the quasi-cocommutativity only. Thus, the quasi-triangular property (and the Yang-Baxter equation!) for the universal R-matrix is a consequence of the linear equation of the quasi-cocommutativity. The proof is based on properties of singular vectors in the tensor product of the Verma modules and the structure of extremal projector for quantized algebras. Explicit expressions of the universal R-matrix for quantized algebras U q (A inf1 sup(1) ) and U q (A inf2 sup(2) ) are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00402899
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 44
    Electronic Resource
    Electronic Resource
    Star-products and phase space realizations of quantum groups (1992)
    Springer
    Letters in mathematical physics 25 (1992), S. 51-59 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 81R50 ; 81S30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is shown for a family of *-products (i.e. different ordering rules) that, under a strong invariance condition, the functions of the quadratic preferred observables (which generate the Cartan subalgebra in phase space realization of Lie algebras) take only the linear or exponential form. An exception occurs for the case of a symmetric ordering *-product where trigonometric functions and two special polynomials can also be included. As an example, the ‘quantized algebra’ of the oscillator Lie algebra is argued.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00402375
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 45
    Electronic Resource
    Electronic Resource
    A natural and rigid model of quantum groups (1992)
    Springer
    Letters in mathematical physics 25 (1992), S. 75-84 
    Details
    ISSN: 1573-0530
    Keywords: 16W30 ; 81R50 ; 17B37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We introduce a natural (Fréchet-Hopf) algebra A containing all generic Jimbo algebras U t (sl(2)) (as dense subalgebras). The Hopf structures on A extend (in a continuous way) the Hopf structures of generic U t (sl(2)). The Universal R-matrices converge in A $$\hat \otimes $$ A. Using the (topological) dual of A, we recover the formalism of functions of noncommutative arguments. In addition, we show that all these Hopf structures on A are isomorphic (as bialgebras), and rigid in the category of bialgebras.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00402377
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 46
    Electronic Resource
    Electronic Resource
    A *-product on SL(2) and the corresponding nonstandard $$(\mathfrak{s}\mathfrak{l}({\text{2}}))$$ (1992)
    Springer
    Letters in mathematical physics 25 (1992), S. 85-88 
    Details
    ISSN: 1573-0530
    Keywords: 16W30 ; 17B37 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We obtain Zakrzewski's deformation of Fun SL(2) through the construction of a *-product on SL(2). We then give the deformation of $$(\mathfrak{s}\mathfrak{l}({\text{2}}))$$ dual to this, as well as a Poincaré basis for both algebras.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00398304
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 47
    Electronic Resource
    Electronic Resource
    Differential geometry on linear quantum groups (1992)
    Springer
    Letters in mathematical physics 25 (1992), S. 139-147 
    Details
    ISSN: 1573-0530
    Keywords: 17B37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract An exterior derivative, inner derivation, and Lie derivative are introduced on the quantum group GL q (N). SL q (N) is then found by constructing matrices with determnant unity, and the induced calculus is found.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00398310
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 48
    Electronic Resource
    Electronic Resource
    Construction of cyclic representations of quantum algebras at q p =1 from their regular representations (1992)
    Springer
    Letters in mathematical physics 25 (1992), S. 277-286 
    Details
    ISSN: 1573-0530
    Keywords: 17B10 ; 17B37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Cyclic representations of maximal dimension of the quantum algebra U q L associated with any finite-dimensional simple Lie algebra L are studied from its regular representation at q p =1, which is proved to be a quotient module of itself as a left module with respect to some submodules. The general theory is given after an instructive example U q sl(2) is studied. Another explicit example U q sl(3) is also presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00398400
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 49
    Electronic Resource
    Electronic Resource
    Finite-dimensional representations of U q (osp(1/2n)) and its connection with quantum so(2n+1) (1992)
    Springer
    Letters in mathematical physics 25 (1992), S. 317-325 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 81R50 ; 17A70
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is shown that the quantum supergroup U q (osp(1/2n)) is essentially isomorphic to the quantum group U -q (so(2n+1)) restricted to tensorial representations. This renders it straightforward to classify all the finite-dimensional irreducible representations of U q (osp(1/2n)) at generic q. In particular, it is proved that at generic q, every-dimensional irrep of this quantum supergroup is a deformation of an osp(1/2n) irrep, and all the finite-dimensional representations are completely reducible.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00398404
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 50
    Electronic Resource
    Electronic Resource
    Fundamental representations of quantum groups at roots of 1 (1992)
    Springer
    Letters in mathematical physics 26 (1992), S. 133-146 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract To every finite-dimensional irreducible representation V of the quantum group Uε(g) where ε is a primitive lth root of unity (l odd) and g is a finite-dimensional complex simple Lie algebra, de Concini, Kac and Procesi have associated a conjugacy class C V in the adjoint group G of g. We describe explicitly, when g is of type A n , B n , C n , or D n , the representations associated to the conjugacy classes of minimal positive dimension. We call such representations fundamental and prove that, for any conjugacy class, there is an associated representation which is contained in a tensor product of fundamental representations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00398810
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 51
    Electronic Resource
    Electronic Resource
    Two variable link polynomials from quantum supergroups (1992)
    Springer
    Letters in mathematical physics 26 (1992), S. 187-198 
    Details
    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract New two variable link polynomials are constructed corresponding to a one-parameter family of representations of the quantum supergroup U q [gl(2 | 1)]. Their connection with the Kauffman polynomials is also investigated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00420752
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 52
    Electronic Resource
    Electronic Resource
    Cohomology and associated deformations for not necessarily co-associative bialgebras (1992)
    Springer
    Letters in mathematical physics 26 (1992), S. 277-283 
    Details
    ISSN: 1573-0530
    Keywords: 16E40 ; 16W30 ; 17B37 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract In this Letter, a cohomology and an associated theory of deformations for (not necessarily co-associative) bialgebras are studied. The cohomology was introduced in a previous paper (Lett. Math. Phys. 25, 75–84 (1992)). This theory has several advantages, especially in calculating cohomology spaces and in its adaptability to deformations of quasi-co-associative (qca) bialgebras and even quasi-triangular qca bialgebras.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00420237
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 53
    Electronic Resource
    Electronic Resource
    Braid group action on theq-Weyl algebra (1991)
    Springer
    Letters in mathematical physics 23 (1991), S. 151-158 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 20F36 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We provide a braid group action on theq-deformed Weyl algebraW q (n). The restriction of this action to the representations ofU q (A n−1 ) andU q (C n ) inW q (n) is seen to agree with the braid group action introduced by Lusztig on these quantum algebras.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00703729
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 54
    Electronic Resource
    Electronic Resource
    On the universalR-matrix for Uq(241-1241-1241-1) (1991)
    Springer
    Letters in mathematical physics 23 (1991), S. 241-250 
    Details
    ISSN: 1573-0530
    Keywords: 81R50 ; 17B37 ; 16W30 ; 81R30 ; 81S05 ; 81T40 ; 20F36
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A compact form for the universalR-matrix of U q (sl n ) is derived and illustrated by simple applications.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01885502
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 55
    Electronic Resource
    Electronic Resource
    Singular vectors of quantum group representations for straight Lie algebra roots (1991)
    Springer
    Letters in mathematical physics 22 (1991), S. 251-266 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 81R50 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We give explicit formulae for singular vectors of Verma modules over Uq(G), where G is any complex simple Lie algebra. The vectors we present correspond exhaustively to a class of positive roots of G which we call straight roots. In some special cases, we give singular vectors corresponding to arbitrary positive roots. For our vectors we use a special basis of Uq(G -), where G - is the negative roots subalgebra of G, which was introducted in our earlier work in the case q=1. This basis seems more economical than the Poincaré-Birkhoff-Witt type of basis used by Malikov, Feigin, and Fuchs for the construction of singular vectors of Verma modules in the case q=1. Furthermore, this basis turns out to be part of a general basis recently introduced for other reasons by Lusztig for Uq(ℬ-), where ℬ- is a Borel subalgebra of G.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00405600
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 56
    Electronic Resource
    Electronic Resource
    Differential calculi on quantum vector spaces with Hecke-type relations (1991)
    Springer
    Letters in mathematical physics 23 (1991), S. 133-141 
    Details
    ISSN: 1573-0530
    Keywords: 81R50 ; 16O80 ; 16W30 ; 17B37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract From a vector spaceV equipped with a Yang-Baxter operatorR one may form the r-symmetric algebraS R V=TV/〈v ⊗w−R(v ⊗w)〉, which is a quantum vector space in the sense of Manin, and the associated quantum matrix algebraM R V=T(End(V))/〈f ⊗g−R(f ⊗g)R -1〉. In the case whenR satisfies a Hecke-type identityR 2=(1−q)R+q, we construct a differential calculus Ω R V forS R V which agrees with that constructed by Pusz, Woronowicz, Wess, and Zumino whenR is essentially theR-matrix of GL q (n). Elements of Ω R V may be regarded as differential forms on the quantum vector spaceS R V. We show that Ω R V isM R V-covariant in the sense that there is a coaction Φ*: Ω R V →M R V ⊗ Ω R V with Φ*d=(1 ⊗ d)Φ* extending the natural coaction Φ:S R V →M R V ⊗S R V.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00703726
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 57
    Electronic Resource
    Electronic Resource
    On a possible origin of quantum groups (1991)
    Springer
    Letters in mathematical physics 22 (1991), S. 155-160 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 81R50 ; 81S30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A Poisson bracket structure having the commutation relations of the quantum group SL q (2) is quantized by means of the Moyal star-product on C ∞(ℝ2), showing that quantum groups are not exactly quantizations, but require a quantization (with another parameter) in the background. The resulting associative algebra is a strongly invariant nonlinear star-product realization of the q-algebra U q (sl(2)). The principle of strong invariance (the requirement that the star-commutator is star-expressed, up to a phase, by the same function as its classical limit) implies essentially the uniqueness of the commutation relations of U q (sl(2)).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00405180
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 58
    Electronic Resource
    Electronic Resource
    Compact quantum groups and group duality (1991)
    Springer
    Acta applicandae mathematicae 25 (1991), S. 277-299 
    Details
    ISSN: 1572-9036
    Keywords: 16S80 ; 17B37 ; 22D25 ; 46L89 ; 47A67 ; Duality ; quantum group ; C *-algebra ; Hopf algebra ; representation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we consider the *-representations of compact quantum groups and group duality. The main results in the paper are: (1) there is a one-to-one correspondence between the *-representations of compact quantum groups and *-representations of the dual Banach *-algebra; (2) the category of commutative compact quantum groups (semigroups) is a dual category to the category of compact groups (semigroups); (3) the dual category of the category of locally compact groups (semigroups) is the category of commutative Hopf C*-algebras with a particular property. Our group duality has the flavor of a Gelfand-Naimark type theorem for compact quantum groups, and for Hopf C*-algebras.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00047006
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...