Vol. 7, No. 6, 2013

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The Picard crossed module of a braided tensor category

Alexei Davydov and Dmitri Nikshych

Vol. 7 (2013), No. 6, 1365–1403
Abstract

For a finite braided tensor category C we introduce its Picard crossed module P(C) consisting of the group of invertible C-module categories and the group of braided tensor autoequivalences of C. We describe P(C) in terms of braided autoequivalences of the Drinfeld center of C. As an illustration, we compute the Picard crossed module of a braided pointed fusion category.

Keywords
braided tensor category, Drinfeld center, braided autoequivalence, invertible module category
Mathematical Subject Classification 2010
Primary: 18D10
Secondary: 16W30
Milestones
Received: 6 February 2012
Revised: 8 November 2012
Accepted: 20 November 2012
Published: 19 September 2013
Authors
Alexei Davydov
Department of Mathematics
Ohio University
Athens, OH 45701
United States
Dmitri Nikshych
Department of Mathematics
University of New Hampshire
Durham, NH 03824
United States