On the Brauer-Picard groups of fusion categories

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.

arXiv comment23 pages, references to arXiv:1407.2783v2 and arXiv:1404.2016 are added, minor corrections