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

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.

5 pages; minor corrections; corollary about Drinfeld twists added

References in corpus (2)

• The Dirac operator on compact quantum groups
• Symmetric invariant cocycles on the duals of q-deformations

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• Classification of ${\mathfrak{sl}}_3$ relations in the Witt group of nondegenerate braided fusion categories
• The group of bi-Galois objects over the coordinate algebra of the Frobenius-Lusztig kernel of SL(2)
• Towards a classification of compact quantum groups of Lie type