On the Brauer-Picard groups of fusion categories

2016/03/14 by Marshall, Ian, Nikshych, Dmitri
#18D10 #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1603.04318

Abstract

We develop methods of computation of the Brauer-Picard groups of fusion categories and apply them to compute such groups for several classes of fusion categories of prime power dimension: representation categories of elementary abelian groups with twisted associativity constraint, extra special p-groups, and the Kac-Paljutkin Hopf algebra. We conclude that many finite groups of Lie type occur as composition factors of the Brauer-Picard groups of pointed fusion categories.

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