Two-Parameter Quantum Groups and Drinfel'd Doubles
نویسندگان
چکیده
منابع مشابه
Two-parameter Quantum Groups and Drinfel’d Doubles
We investigate two-parameter quantum groups corresponding to the general linear and special linear Lie algebras gln and sln. We show that these quantum groups can be realized as Drinfel’d doubles of certain Hopf subalgebras with respect to Hopf pairings. Using the Hopf pairing, we construct a corresponding R-matrix. The quantum groups have a natural n-dimensional module V . The R-matrix enables...
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We report on two classes of autoequivalences of the category of Yetter-Drinfeld modules over a finite group, or, equivalently the Drinfeld center of the category of representations of a finite group. Both operations are related to the r-th power operation, with r relatively prime to the exponent of the group. One is defined more generally for the group-theoretical fusion category defined by a f...
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We determine the finite-dimensional simple modules for two-parameter quantum groups corresponding to the general linear and special linear Lie algebras gl n and sln, and give a complete reducibility result. These quantum groups have a natural n-dimensional module V . We prove an analogue of Schur-Weyl duality in this setting: the centralizer algebra of the quantum group action on the k-fold ten...
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We investigate the fine structure of the symplectic foliations of Poisson homogeneous spaces. Two general results are proved for weak splittings of surjective Poisson submersions from Heisenberg and Drinfeld doubles. The implications of these results are that the torus orbits of symplectic leaves of the quotients can be explicitly realized as Poisson–Dirac submanifolds of the torus orbits of th...
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We investigate the braid group representations arising from categories of representations of twisted quantum doubles of finite groups. For these categories, we show that the resulting braid group representations always factor through finite groups, in contrast to the categories associated with quantum groups at roots of unity. We also show that in the case of p-groups, the corresponding pure br...
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ژورنال
عنوان ژورنال: Algebras and Representation Theory
سال: 2004
ISSN: 1386-923X
DOI: 10.1023/b:alge.0000031151.86090.2e