Representation rings of quantum groups

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dc.creatorDomokos, M.
dc.creatorLenagan, T. H.
dc.date2003-08-29
dc.date.accessioned2026-07-07T05:00:41Z
dc.date.available2026-07-07T05:00:41Z
dc.descriptionGenerators and relations are given for the subalgebra of cocommutative elements in the quantized coordinate rings of the classical groups, where the deformation parameter q is transcendental. This is a ring theoretic formulation of the well known fact that the representation theory of the quantized group is completely analogous to its classical counterpart. The subalgebras of cocommutative elements in the corresponding FRT-bialgebras (defined by Faddeev, Reshetikhin, and Takhtadzhyan) are explicitly determined, using a bialgebra embedding of the FRT-bialgebra into the tensor product of the quantized coordinate ring and the one-variable polynomial ring. A parallel analysis of the subalgebras of adjoint coinvariants is carried out as well, yielding similar results with similar proofs. The basic adjoint coinvariants are interpreted as quantum traces of representations of the corresponding quantized universal enveloping algebra.
dc.description29 pages
dc.identifierhttps://arxiv.org/abs/math/0308289
dc.identifierhttp://arxiv.org/abs/math/0308289
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/68411
dc.subjectQuantum Algebra
dc.subjectRings and Algebras
dc.subject20G42; 16W30
dc.titleRepresentation rings of quantum groups
dc.typetext

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