On the Brauer-Picard groups of fusion categories
Quantum Algebra
2016-10-26 v3
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.
Keywords
Cite
@article{arxiv.1603.04318,
title = {On the Brauer-Picard groups of fusion categories},
author = {Ian Marshall and Dmitri Nikshych},
journal= {arXiv preprint arXiv:1603.04318},
year = {2016}
}
Comments
23 pages, references to arXiv:1407.2783v2 and arXiv:1404.2016 are added, minor corrections