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  • Articles  (85)
  • 81R50  (58)
  • 16W30  (55)
  • 1990-1994  (85)
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  • Mathematics  (85)
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  • Articles  (85)
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  • Mathematics  (85)
  • Architecture, Civil Engineering, Surveying
  • Physics  (84)
  • 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
    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
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  • 5
    Electronic Resource
    Electronic Resource
    The Hamiltonian systems on the Poisson structure of the quasi-classical limit of GL q (∞) (1991)
    Springer
    Letters in mathematical physics 23 (1991), S. 121-126 
    Details
    ISSN: 1573-0530
    Keywords: 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We consider the Hamiltonian systems on the Poisson structure of GL(∞) which is introduced from the quantum group GL q (∞) by the so-called quasi-classical limit of GL q (∞). Furthermore, we show that the Toda lattice hierarchy is a Hamiltonian system of this structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00703724
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  • 6
    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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  • 7
    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
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  • 8
    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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  • 9
    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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  • 10
    Electronic Resource
    Electronic Resource
    Quantum E(2) group and its Pontryagin dual (1991)
    Springer
    Letters in mathematical physics 23 (1991), S. 251-263 
    Details
    ISSN: 1573-0530
    Keywords: 81R50 ; 22D25 ; 22D35
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The quantum deformation of the group of motions of the plane and its Pontryagin dual are described in detail. It is shown that the Pontryagin dual is a quantum deformation of the group of transformations of the plane generated by translations and dilations. An explicit expression for the unitary bicharacter describing the Pontryagin duality is found. The Heisenberg commutation relations are written down.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00398822
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