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dc.contributor.authorTuset, Lars
dc.contributor.authorNeshveyev, Sergey
dc.date.accessioned2012-01-06T12:23:44Z
dc.date.available2012-01-06T12:23:44Z
dc.date.issued2011-09
dc.identifier.citationTuset, L. & Neshveyev, S. (2011). On second cohomology of duals of compact quantum groups. International Journal of Mathematics, 22 (9), 1231-1260.en_US
dc.identifier.issnPrint: 0129-167X
dc.identifier.issnOnline: 1793-6519
dc.identifier.otherFRIDAID 843349
dc.identifier.urihttps://hdl.handle.net/10642/1022
dc.description.abstractWe show that for any compact connected group G the second cohomology group de ned by unitary invariant 2-cocycles on ^G is canonically isomorphic to H2(\Z(G); T). This implies that the group of autoequivalences of the C -tensor category RepG is isomorphic to H2(\Z(G); T) o Out(G). We also show that a compact connected group G is completely determined by RepG. More generally, extending a result of Etingof-Gelaki and Izumi-Kosaki we describe all pairs of compact separable monoidally equivalent groups. The proofs rely on the theory of ergodic actions of compact groups developed by Landstad and Wassermann and on its algebraic counterpart developed by Etingof and Gelaki for the classi cation of triangular semisimple Hopf algebras. In two appendices we give a self-contained account of amenability of tensor categories, fusion rings and discrete quantum groups, and prove an analogue of Radford's theorem on minimal Hopf subalgebras of quasitriangular Hopf algebras for compact quantum groups.en_US
dc.description.sponsorshipSupported by the Research Council of Norway.
dc.language.isoengen_US
dc.publisherWorld Scientific Publishingen_US
dc.relation.ispartofseriesInternational Journal of Mathematics;22 (9)
dc.subjectCompact groupsen_US
dc.subjectDual cocyclesen_US
dc.subjectTensor categoriesen_US
dc.subjectAMSC numbersen_US
dc.subject46L40en_US
dc.subject18D10en_US
dc.subject20G42en_US
dc.subjectVDP::Matematikk og Naturvitenskap: 400::Matematikk: 410en_US
dc.titleOn second cohomology of duals of compact quantum groupsen_US
dc.typeJournal articleen_US
dc.typePeer revieweden_US
dc.identifier.doihttp://dx.doi.org/10.1142/S0129167X11007239


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