The Picard crossed module of a braided tensor category

Davydov, Alexei; Nikshych, Dmitri

doi:10.2140/ant.2013.7.1365

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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

DOI: 10.2140/ant.2013.7.1365

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

Vol. 7, No. 6, 2013