Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area Let (H,R) be a finite dimensional quasitriangular Hopf algebra over a field k, and HM the representation category of H. In this paper, we study the braided autoequivalences of the Drinfeld center HHYD trivializable on HM. We establish a group isomorphism between the group of those autoequivalences and the group of quantum commutative bi-Galois objects of the transmutation braided Hopf algebra RH. We then apply this isomorphism to obtain a categorical interpretation of the exact sequence of the equivariant Brauer group BM(k,H,R) established by Zhang. To this end, we have to develop the braided bi-Galois theory initiated by Schauenburg, which generalizes the Hopf bi-Galois theory over usual Hopf algebras to the one over braided Hopf algebras in a braided monoidal category. Recording during the thematic meeting: "Algebra, deformations and quantum groups " the December 4, 2014 at the Centre International de Rencontres Mathématiques (Marseille, France)

• published: 10 Aug 2015
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