Crossed pointed categories and their equivariantizations

Deepak Naidu

Vol. 247 (2010), No. 2, 477–496

DOI: 10.2140/pjm.2010.247.477

Abstract

We propose a notion, quasiabelian third cohomology of crossed modules, which generalizes Eilenberg and Mac Lane’s abelian and Ospel’s quasiabelian cohomology. We classify crossed pointed categories in terms of it. We apply the process of equivariantization to the latter to obtain braided fusion categories, which may be viewed as generalizations of the categories of modules over twisted Drinfeld doubles of finite groups. As a consequence, we obtain a description of all braided group-theoretical categories. We give a criterion for these categories to be modular. We describe the quasitriangular quasi-Hopf algebras underlying these categories.

Keywords

braided crossed G-categories, equivariantization, group-theoretical fusion categories

Mathematical Subject Classification 2000

Primary: 18D10

Secondary: 16W30

Milestones

Received: 1 June 2009

Revised: 17 May 2010

Accepted: 24 May 2010

Published: 11 August 2010