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  • Articles  (15)
  • Articles: DFG German National Licenses  (15)
  • 16W30  (15)
  • 1990-1994  (15)
  • 1965-1969
  • 1994  (15)
  • Mathematics  (15)
  • Architecture, Civil Engineering, Surveying
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  • Articles  (15)
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  • Articles: DFG German National Licenses  (15)
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  • 1990-1994  (15)
  • 1965-1969
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  • Mathematics  (15)
  • Architecture, Civil Engineering, Surveying
  • Physics  (14)
  • 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
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  • 2
    Electronic Resource
    Electronic Resource
    The quantum de Rham complexes associated with SL h (2) (1994)
    Springer
    Letters in mathematical physics 30 (1994), S. 87-98 
    Details
    ISSN: 1573-0530
    Keywords: 16W30 ; 16S80 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Quantum de Rham complexes on the quantum plane and the quantum group itself are constructed for the nonstandard deformation of Fun(SL(2)). It is shown that in contrast to the standardq-deformation of SL(2), the above complexes are unique for SL h (2). Also, as a byproduct, a new deformation of the two-dimensional Heisenberg algebra is obtained which can be used to construct models ofh-deformed quantum mechanics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939696
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  • 3
    Electronic Resource
    Electronic Resource
    Differential calculus on the inhomogeneous quantum groups IGL q (n) (1994)
    Springer
    Letters in mathematical physics 30 (1994), S. 233-239 
    Details
    ISSN: 1573-0530
    Keywords: 16W30 ; 22E70 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We obtain the inhomogeneousq-groups IGL q (n) via a projection from GL q (n + 1). The bicovariant differential calculus of IGL q (n) is constructed, and the corresponding quantum Lie algebra is given explicitly.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00805855
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  • 4
    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
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  • 5
    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
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  • 6
    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
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  • 7
    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
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  • 8
    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
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  • 9
    Electronic Resource
    Electronic Resource
    Existence of a Lie bialgebra structure on every Lie algebra (1994)
    Springer
    Letters in mathematical physics 31 (1994), S. 225-231 
    Details
    ISSN: 1573-0530
    Keywords: 16W30 ; 17Bxx
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We prove that every non-Abelian, finite-dimensional Lie algebra admits an exact bialgebra structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00761714
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  • 10
    Electronic Resource
    Electronic Resource
    SU q (2) covariant $$\hat R$$ -matrices for reducible representations (1994)
    Springer
    Letters in mathematical physics 31 (1994), S. 279-288 
    Details
    ISSN: 1573-0530
    Keywords: 16W30 ; 81R05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We consider SU q (2) covariant $$\hat R$$ -matrices for the reducible3 ⊕1 representation. There are three solutions to the Yang-Baxter equation. They coincide with the previously known $$\hat R$$ -matrices for SO q (3) and SO q (3, 1). Also, they are the three $$\hat R$$ -matrices which can be constructed by using four different SU q (2) doublets. Only two of the three $$\hat R$$ -matrices allow a differential structure on the reducible four-dimensional quantum space.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00762790
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