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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. dellojeroen@gmail.com; yinhuo.zhang@uhasselt.be | Keywords: | Brauer group; Hopf algebra; braided autoequivalence | Document URI: | http://hdl.handle.net/1942/19649 | 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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braided autoequivalences and the Brauer group of a QT Hopf algebra.pdf Restricted Access | Published version | 1.01 MB | Adobe PDF | View/Open Request a copy |
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