Autoequivalences of the tensor category of Uq(g)-modules
Quantum Algebra
2013-05-29 v3 Operator Algebras
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.
Cite
@article{arxiv.1012.4700,
title = {Autoequivalences of the tensor category of Uq(g)-modules},
author = {Sergey Neshveyev and Lars Tuset},
journal= {arXiv preprint arXiv:1012.4700},
year = {2013}
}
Comments
5 pages; minor corrections; corollary about Drinfeld twists added