Open Access
2013 The Picard crossed module of a braided tensor category
Alexei Davydov, Dmitri Nikshych
Algebra Number Theory 7(6): 1365-1403 (2013). DOI: 10.2140/ant.2013.7.1365


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.


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Alexei Davydov. Dmitri Nikshych. "The Picard crossed module of a braided tensor category." Algebra Number Theory 7 (6) 1365 - 1403, 2013.


Received: 6 February 2012; Revised: 8 November 2012; Accepted: 20 November 2012; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1284.18015
MathSciNet: MR3107567
Digital Object Identifier: 10.2140/ant.2013.7.1365

Primary: 18D10
Secondary: 16W30

Keywords: braided autoequivalence , braided tensor category , Drinfeld center , invertible module category

Rights: Copyright © 2013 Mathematical Sciences Publishers

Vol.7 • No. 6 • 2013
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