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arXiv · 1012.4700

Autoequivalences of the tensor category of Uq(g)-modules

Sergey Neshveyev·Lars Tuset
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Abstract

We prove that for q\in\C* not a nontrivial root of unity the cohomology group defined by invariant 2-cocycles in a completion of Uq(g) is isomorphic to H^2(P/Q;\T), where P and Q are the weight and root lattices of g. This implies that the group of autoequivalences of the tensor category of Uq(g)-modules is the semidirect product of H^2(P/Q;\T) and the automorphism group of the based root datum of g. For q=1 we also obtain similar results for all compact connected separable groups.

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Sergey Neshveyev, Lars Tuset. 2010-12-21. Autoequivalences of the tensor category of Uq(g)-modules. https://doi.org/10.1093/imrn%2Frnr151

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