dc.contributor.author | Tuset, Lars | |
dc.contributor.author | Neshveyev, Sergey | |
dc.date.accessioned | 2012-01-06T12:23:44Z | |
dc.date.available | 2012-01-06T12:23:44Z | |
dc.date.issued | 2011-09 | |
dc.identifier.citation | Tuset, 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.issn | Print: 0129-167X | |
dc.identifier.issn | Online: 1793-6519 | |
dc.identifier.other | FRIDAID 843349 | |
dc.identifier.uri | https://hdl.handle.net/10642/1022 | |
dc.description.abstract | We 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.sponsorship | Supported by the Research Council of Norway. | |
dc.language.iso | eng | en_US |
dc.publisher | World Scientific Publishing | en_US |
dc.relation.ispartofseries | International Journal of Mathematics;22 (9) | |
dc.subject | Compact groups | en_US |
dc.subject | Dual cocycles | en_US |
dc.subject | Tensor categories | en_US |
dc.subject | AMSC numbers | en_US |
dc.subject | 46L40 | en_US |
dc.subject | 18D10 | en_US |
dc.subject | 20G42 | en_US |
dc.subject | VDP::Matematikk og Naturvitenskap: 400::Matematikk: 410 | en_US |
dc.title | On second cohomology of duals of compact quantum groups | en_US |
dc.type | Journal article | en_US |
dc.type | Peer reviewed | en_US |
dc.identifier.doi | http://dx.doi.org/10.1142/S0129167X11007239 | |