Notes on the Kazhdan-Lusztig theorem on equivalence of the Drinfeld category and the category of Uq(g)-modules

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dc.creatorNeshveyev, Sergey
dc.creatorTuset, Lars
dc.date2007-11-27
dc.date.accessioned2026-07-07T08:45:24Z
dc.date.available2026-07-07T08:45:24Z
dc.descriptionWe discuss the proof of Kazhdan and Lusztig of the equivalence of the Drinfeld category D(g,h) of g-modules and the category of finite dimensional Uq(g)-modules, q=exp(πih), for h\in C\Q*. Aiming at operator algebraists the result is formulated as the existence for each h\in iR of a normalized unitary 2-cochain F on the dual \hat G of a compact simple Lie group G such that the convolution algebra of G with the coproduct twisted by F is *-isomorphic to the convolution algebra of the q-deformation G_q of G, while the coboundary of F^{-1} coincides with Drinfeld's KZ-associator defined via monodromy of the Knizhnik-Zamolodchikov equations.
dc.description40 pages
dc.identifierhttps://arxiv.org/abs/0711.4302
dc.identifierhttp://arxiv.org/abs/0711.4302
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/142954
dc.subjectQuantum Algebra
dc.subjectOperator Algebras
dc.titleNotes on the Kazhdan-Lusztig theorem on equivalence of the Drinfeld category and the category of Uq(g)-modules
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