Twisting the q-deformations of compact semisimple Lie groups

Abstract

Given a compact semisimple Lie group $G$ of rank $r$, and a parameter $q>0$, we can define new associativity morphisms in Rep(Gq) using a 3-cocycle $\Phi$ on the dual of the center of G, thus getting a new tensor category Rep(Gq)${}^{\Phi }$. For a class of cocycles $\Phi$ we construct compact quantum groups $G_q^{\tau }$ with representation categories Rep(Gq)${}^{\Phi }$. The construction depends on the choice of an r-tuple $\tau$ of elements in the center of G. In the simplest case of G=SU(2) and $\tau =-1$, our construction produces Woronowicz's quantum group SU_{-q}(2) out of SUq(2). More generally, for G=SU(n), we get quantum group realizations of the Kazhdan-Wenzl categories.

20 pages; remark on braiding, minor modifications

References in corpus (1)

• Equivariant comparison of quantum homogeneous spaces

Cited by in corpus (6)

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• Towards a classification of compact quantum groups of Lie type
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