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  • Articles  (55)
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  • Articles  (55)
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  • Mathematics  (55)
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  • Physics  (54)
  • 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
    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
    Keywords: 16W30 ; 81R05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00402900
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  • 3
    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
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  • 4
    Electronic Resource
    Electronic Resource
    On the defining relations of quantum superalgebras (1991)
    Springer
    Letters in mathematical physics 23 (1991), S. 127-131 
    Details
    ISSN: 1573-0530
    Keywords: 16W30 ; 16S80 ; 22E70
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00703725
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  • 5
    Electronic Resource
    Electronic Resource
    Six generatorq-deformed Lorentz algebra (1991)
    Springer
    Letters in mathematical physics 23 (1991), S. 233-240 
    Details
    ISSN: 1573-0530
    Keywords: 16W30 ; 81R05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01885501
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  • 6
    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
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  • 7
    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
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  • 8
    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
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  • 9
    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
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  • 10
    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
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