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  • Artikel  (55)
  • 16W30  (55)
  • 1990-1994  (55)
  • 1965-1969
  • Mathematik  (55)
  • Architektur, Bauingenieurwesen, Vermessung
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  • Artikel  (55)
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  • Mathematik  (55)
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  • Physik  (54)
  • 1
    Digitale Medien
    Digitale Medien
    Quantum homogeneous spaces, duality and quantum 2-spheres (1994)
    Springer
    Geometriae dedicata 52 (1994), S. 291-315 
    Details
    ISSN: 1572-9168
    Schlagwort(e): 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
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01278478
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  • 2
    Digitale Medien
    Digitale Medien
    Differential operators on quantum spaces for GL q (n) and SO q (n) (1992)
    Springer
    Letters in mathematical physics 24 (1992), S. 245-255 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 16W30 ; 81R05
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract We prove that the rings of q-differential operators on quantum planes of the GL q (n) and SO q (n) types are isomorphic to the rings of classical differential operators. Also, we construct decompositions of the rings of q-differential operators into tensor products of the rings of q-differential operators with less variables.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00402900
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  • 3
    Digitale Medien
    Digitale Medien
    Simple WZW superselection sectors (1993)
    Springer
    Letters in mathematical physics 28 (1993), S. 31-41 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 16W30 ; 17B37 ; 81T05
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00739564
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  • 4
    Digitale Medien
    Digitale Medien
    On the defining relations of quantum superalgebras (1991)
    Springer
    Letters in mathematical physics 23 (1991), S. 127-131 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 16W30 ; 16S80 ; 22E70
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract In defining quantum superalgebras, extra relations need to be added to the Serre-like relations. They are obtained for sl q (m, n) and osp q (m, 2n) usingq-oscillator representations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00703725
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  • 5
    Digitale Medien
    Digitale Medien
    Six generatorq-deformed Lorentz algebra (1991)
    Springer
    Letters in mathematical physics 23 (1991), S. 233-240 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 16W30 ; 81R05
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract The six generator deformation of the Lorentz algebra is presented. The Hopf algebra structure and the reality conditions are found. The chiral decomposition of SL(2, C) is generalized to theq-case. Casimir operators for theq-Lorentz algebra are given.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01885501
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  • 6
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): 81R50 ; 17B37 ; 16W30 ; 81R30 ; 81S05 ; 81T40 ; 20F36
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract A compact form for the universalR-matrix of U q (sl n ) is derived and illustrated by simple applications.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01885502
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  • 7
    Digitale Medien
    Digitale Medien
    Quantum groups and diagonalization of the braid generator (1992)
    Springer
    Letters in mathematical physics 24 (1992), S. 183-196 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 81R10 ; 17B37 ; 16W30
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00402893
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  • 8
    Digitale Medien
    Digitale Medien
    Serre-type relations for special linear Lie superalgebras (1992)
    Springer
    Letters in mathematical physics 24 (1992), S. 173-181 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 17A70 ; 16W30 ; 17B37 ; 81R50
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00402892
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  • 9
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): 81R10 ; 17B37 ; 16W30
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract A new quantum double is established from a new Hopf algebra and a new kind of quantum R-matrix is obtained.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00402894
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  • 10
    Digitale Medien
    Digitale Medien
    The double of a Jacobian quasi-bialgebra (1993)
    Springer
    Letters in mathematical physics 28 (1993), S. 13-29 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 17B37 ; 16W30 ; 17B70
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00739563
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