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  • Mathematik  (24)
  • 1
    Digitale Medien
    Digitale Medien
    Braided Hopf algebras and differential calculus (1995)
    Springer
    Letters in mathematical physics 33 (1995), S. 33-38 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 17B37 ; 81R50
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract We show that the algebra of the bicovariant differential calculus on a quantum group can be understood as a projection of the cross-product between a braided Hopf algebra and the quantum double of the quantum group. The resulting super-Hopf algebra can be reproduced by extending the exterior derivative to tensor products.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00750809
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  • 2
    Digitale Medien
    Digitale Medien
    Lie groups whose coadjoint orbits are of dimension smaller or equal to two (1995)
    Springer
    Letters in mathematical physics 33 (1995), S. 183-186 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 16W30 ; 17Bxx ; 17B05 ; 81R50
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract We give a complete classification of the class of connected, simply connected Lie groups whose coadjoint orbits are of dimension smaller or equal to two.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00739806
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  • 3
    Digitale Medien
    Digitale Medien
    Integration over the group space of SUq(2), Clebsch-Gordan coefficients, and related identities (1995)
    Springer
    Letters in mathematical physics 33 (1995), S. 221-229 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 81R50 ; 17B37
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract We calculate the Clebsch-Gordan coefficients of SUq(2) by a Woronowicz integration over the group manifold and obtain a representation differing from that reached by working with theq-group algebra. These apparently different results must agree, however, and their equivalence implies aq-identity. On lettingq = 1, we shall obtain two results of different structures for the Clebsch-Gordan coefficients of SU(2) and their equivalence similarly implies an identity among the usual binomial coefficients. With the same approach, one may extend the Woronowicz integral of the product of two irreducible representations to products of many irreducible representations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00749623
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  • 4
    Digitale Medien
    Digitale Medien
    Fock spaces with generalized statistics (1995)
    Springer
    Letters in mathematical physics 33 (1995), S. 283-295 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 81T05 ; 81R50 ; 81S05
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract Fock representations for quantum fields which obey generalized statistics are explicitly constructed. The main features of these representations are investigated.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00749682
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  • 5
    Digitale Medien
    Digitale Medien
    Cohomology and deformation of Leibniz pairs (1995)
    Springer
    Letters in mathematical physics 34 (1995), S. 77-90 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 16E40 ; 16W30 ; 17B37 ; 81R50
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract Cohomology and deformation theories are developed for Poisson algebras starting with the more general concept of a Leibniz pair, namely of an associative algebraA together with a Lie algebraL mapped into the derivations ofA. A bicomplex (with both Hochschild and Chevalley-Eilenberg cohomologies) is essential.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00739377
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  • 6
    Digitale Medien
    Digitale Medien
    BRST structures and symplectic geometry on a class of supermanifolds (1995)
    Springer
    Letters in mathematical physics 33 (1995), S. 207-219 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 81R50 ; 17B37 ; 58A50 ; 81Q60
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract By investigating the symplectic geometry and geometric quantization of a class of supermanifolds, we exhibit BRST structures for a certain kind of algebras. We discuss the undeformed andq-deformed cases in the classical as well as in the quantum cases.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00749622
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  • 7
    Digitale Medien
    Digitale Medien
    A star-product approach to noncompact quantum groups (1995)
    Springer
    Letters in mathematical physics 33 (1995), S. 231-240 
    Details
    ISSN: 1573-0530
    Schlagwort(e): AMS classification 17B37 ; 16W30 ; 22D05 ; 46H99 ; 81R50
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract Using the duality and the topological theory of well-behaved Hopf algebras, we construct star-product models of noncompact quantum groups from Drinfeld and Reshetikhin standard deformations of enveloping Hopf algebras of simple Lie algebras. Our star-products act not only on coefficient functions of finite-dimensional representations, but actually on allC ∞ functions, and they even exist for nonlinear (semi-simple) Lie groups.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00749624
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  • 8
    Digitale Medien
    Digitale Medien
    Projective quantum spaces (1995)
    Springer
    Letters in mathematical physics 35 (1995), S. 91-97 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 81R50 ; 14M15 ; 14M17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract Associated to the standard SU q (n) R-matrices, we introduce quantum spheresS q 2n-1 , projective quantum spaces ℂℙ q n-1 , and quantum Grassmann manifoldsG k(ℂ q n ). These algebras are shown to be homogeneous spaces of standard quantum groups and are also quantum principle bundles in the sense of T. Brzeziński and S. Majid.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00750759
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  • 9
    Digitale Medien
    Digitale Medien
    Noncommutative symmetric functions and laplace operators for classical Lie algebras (1995)
    Springer
    Letters in mathematical physics 35 (1995), S. 135-143 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 17B35 ; 17B37 ; 81R50
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract New systems of Laplace (Casimir) operators for the orthogonal and symplectic Lie algebras are constructed. The operators are expressed in terms of paths in graphs related to matrices formed by the generators of these Lie algebras with the use of some properties of the noncommutative symmetric functions associated with a matrix. The decomposition of the Sklyanin determinant into a product of quasi-determinants play the main role in the construction. Analogous decomposition for the quantum determinant provides an alternative proof of the known construction for the Lie algebra gl(N).
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00750763
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  • 10
    Digitale Medien
    Digitale Medien
    Bicovariant differential geometry of the quantum group SL h (2) (1995)
    Springer
    Letters in mathematical physics 35 (1995), S. 303-311 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 81R50 ; 16W30 ; 58B30
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract There are only two quantum group structures on the space of two by two unimodular matrices, these are the SL q (2) and the SL h (2) quantum groups. The differential geometry of SL q (2) is well known. In this Letter, we develop the differential geometry of SL h (2), and show that the space of left invariant vector fields is three-dimensional.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00750837
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  • 11
    Digitale Medien
    Digitale Medien
    Quantum algebras for maximal motion groups ofN-dimensional flat spaces (1995)
    Springer
    Letters in mathematical physics 33 (1995), S. 273-281 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 17B37 ; 81R50 ; 16W30
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract An embedding method to getq-deformations for the nonsemisimple algebras generating the motion groups ofN-dimensional flat spaces is presented. This method gives a global and simultaneous scheme ofq-deformation for all iso(p, q) algebras and for those obtained from them by some Inönü-Wigner contractions, such as theN-dimensional Euclidean, Poincaré, and Galilei algebras.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00749681
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  • 12
    Digitale Medien
    Digitale Medien
    GL q (N)-covariant braided differential bialgebras (1995)
    Springer
    Letters in mathematical physics 33 (1995), S. 297-302 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 81R50
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract We study the possibility of defining the (braided) comultiplication for the GL q (N)-covariant differential complexes on some quantum spaces. We discover suchdifferential bialgebras (and Hopf algebras) on the bosonic and fermionic quantum hyperplanes (with additive coproduct) and on the braided matrix algebra BM q (N) with both multiplicative and additive coproducts. The latter case is related (forN = 2) to theq-Minkowski space andq-Poincaré algebra.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00749683
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  • 13
    Digitale Medien
    Digitale Medien
    A quantum dual pair $$\mathfrak{s}\mathfrak{l}_2 ,\mathfrak{o}_n $$ and the associated Capelli identity (1995)
    Springer
    Letters in mathematical physics 34 (1995), S. 1-8 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 17B37 ; 81R50
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract A quantum analogue of the dual pair $$\mathfrak{s}\mathfrak{l}_2 ,\mathfrak{o}_n $$ is introduced in terms of the oscillator representation of U q $$(\mathfrak{s}\mathfrak{l}_2 )$$ . Its commutant and the associated identity of Capelli type are discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00739369
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  • 14
    Digitale Medien
    Digitale Medien
    Deformations of multiparameter quantum gl(N) (1995)
    Springer
    Letters in mathematical physics 34 (1995), S. 25-36 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 81R50 ; 70G50
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract Multiparameter quantum gl(N) is not a rigid structure. This Letter defines an essential deformation as one that cannot be interpreted in terms of a similarity transformation, nor as a perturbation of the parameters. All the equivalence classes of first-order essential deformations are found, as well as a class of exact deformations. This work provides quantization of all the classical Lie bialgebra structures (constantr-matrices) found by Belavin and Drinfeld for sl(n). A special case, that requires the Hecke parameter to be a cubic root of unity, stands out.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00739372
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  • 15
    Digitale Medien
    Digitale Medien
    On the schwarz problem for the $$\widehat{{\text{su}}}_{\text{2}} $$ Knizhnik-Zamolodchikov equation (1995)
    Springer
    Letters in mathematical physics 35 (1995), S. 123-134 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 81T40 ; 81R10 ; 81R50
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract We study the monodromy representationsℬ k,Iof the mapping class groupℬ 4 acting on 4-point blocks satisfying the Knizhnik-Zamolodchikov equation for the levelk su2 current algebra. We classify all irreducibleℬ k,Iwhich are realized by finite groups; we also display finite irreducible components for the reducible representations corresponding tok = 10.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00750762
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  • 16
    Digitale Medien
    Digitale Medien
    Coherent states of theq-Weyl algebra (1995)
    Springer
    Letters in mathematical physics 35 (1995), S. 179-185 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 17B37 ; 33D80 ; 81R50
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract New coherent states of theq-Weyl algebraAA † −qA † A = 1,0 〈q 〈 1, are constructed. They are defined as eigenstates of the operatorA † which is the lowering operator for nonhighest weight representations describing positive energy states. Depending on whether the positive spectrum is discrete or continuous, these coherent states are related either to the bilateral basic hypergeometric series or to some integrals over them. The free particle realization of theq-Weyl algebra whenA † A ∞ d2/dx2 is used for illustrations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00750767
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  • 17
    Digitale Medien
    Digitale Medien
    q-transformation theory (1995)
    Springer
    Letters in mathematical physics 35 (1995), S. 221-227 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 81R50 ; 81S05 ; 81P99
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract We obtain the complete set of states of theq-oscillator in both configuration space and momentum space as well as the transformation between these spaces. The states as well as the matrix elements lie in the SU q (2) algebra. To obtain transition probabilities, one must take the ‘Woronowicz square.’
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00761294
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  • 18
    Digitale Medien
    Digitale Medien
    The quantum super-Yangian and Casimir operators of Uq(gl(M |N)) (1995)
    Springer
    Letters in mathematical physics 33 (1995), S. 263-272 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 17B37 ; 81R50 ; 17A70
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract TheZ 2 graded Yangian Yq(gl(M |N)) associated with the Perk-SchultzR matrix is introduced. Its structural properties, the central algebra in particular, are studied. AZ 2-graded associative algebra epimorphism Yq(gl(M |N)) → Uq (gl(M |N)) is obtained in explicit form. Images of central elements of the quantum super-Yangian under this epimorphism yield the Casimir operators of the quantum supergroup Uq(gl(M |N)) constructed in an earlier publication.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00749628
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  • 19
    Digitale Medien
    Digitale Medien
    The two-dimensional Euclidean quantum algebra at roots of unity (1995)
    Springer
    Letters in mathematical physics 34 (1995), S. 37-48 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 16S32 ; 81R50
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract The two-dimensional Euclidean quantum algebra is considered at roots of unity. The algebraic properties and the Poisson-Hopf structure are first investigated. We then determine the irreducible representations and study the reduction of the tensor product of two of them.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00739373
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  • 20
    Digitale Medien
    Digitale Medien
    Transformation theory ofq-quantum mechanics (1995)
    Springer
    Letters in mathematical physics 34 (1995), S. 275-283 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 81P99 ; 81R50 ; 81S05
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract Although there is no empirical motivation for replacing the commutators of dynamically conjugate operators in quantum mechanics byq-commutators, it appears possible to construct a consistent mathematical formulism based on this idea. To examine such a possibility further, we have studied the relation of this proposal to the Schwinger action principle, since the entire quantum mechanical formulism may be inferred from this principle. In particular, we have discussed the quantum transformation theory within this framework.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01872781
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  • 21
    Digitale Medien
    Digitale Medien
    Interrelations between quantum groups and reflection equation (braided) algebras (1995)
    Springer
    Letters in mathematical physics 34 (1995), S. 333-341 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 81R50
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract We show that the differential complex Ω B over the braided matrix algebra BM q (N) represents a covariant comodule with respect to the coaction of the Hopf algebra Ω A which is a differential extension of GL q (N). On the other hand, the algebra Ω A is a covariant braided comodule with respect to the coaction of the braided Hopf algebra Ω B . Geometrical aspects of these results are discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00750065
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  • 22
    Digitale Medien
    Digitale Medien
    Unitary group representations in fock spaces with generalized exchange properties (1995)
    Springer
    Letters in mathematical physics 35 (1995), S. 163-177 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 81T05 ; 81R05 ; 81R50
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract We investigate the notion of secondR-quantization - a suitable deformation of the standard second quantization which properly takes into account the nontrivial exchange properties characterizing generalized statistics. We also perform theR-quantization of a class of unitary one-particle representations relevant for the description of symmetries. The Euclidean covariance of anyons is analyzed within this context.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00750766
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