{"paper":{"title":"Autoequivalences of the tensor category of Uq(g)-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.QA","authors_text":"Lars Tuset, Sergey Neshveyev","submitted_at":"2010-12-21T15:47:07Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4700","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}