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Title: Braided autoequivalences and the equivariant Brauer group of a quasitriangular Hopf algebra
Authors: DELLO, Jeroen 
ZHANG, Yinhuo 
Issue Date: 2016
Source: JOURNAL OF ALGEBRA, 445, p. 244-279
Abstract: Let (H, R)be a finite dimensional quasitriangular Hopf al-gebra over a field k, and HMthe representation category ofH. In this paper, we study the braided autoequivalences of the Drinfeld center HHYDtrivializable on HM. We establish a group isomorphism between the group of those autoequiv-alences 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 inter-pretation of the exact sequence of the equivariant Brauer group BM(k, H, R)in [18]. To this aim, we have to develop the braided bi-Galois theory established by Schauenburg in [14,15], which generalizes the Hopf bi-Galois theory over usual Hopf algebras to the one over braided Hopf algebras in a braided monoidal category.
Notes: Zhang, YH (reprint author), Univ Hasselt, Dept Math, Agoralaan 1, B-3590 Diepenbeek, Belgium.;
Keywords: Brauer group; Hopf algebra; braided autoequivalence
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ISSN: 0021-8693
e-ISSN: 1090-266X
DOI: 10.1016/j.jalgebra.2015.08.005
ISI #: 000365826900013
Rights: © 2015 Elsevier Inc. All rights reserved.
Category: A1
Type: Journal Contribution
Validations: ecoom 2016
Appears in Collections:Research publications

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