Crossed pointed categories and their equivariantizations

Details Crossed pointed categories and their equivariantizations Crossed pointed categories and their equivariantizations

2011-11-22

arxiv.org/abs/1111.5246v1

Pacific J. Math. 247 (2010), no. 2, 477-496

Mathematics

Quantum Algebra

18 pages

Scientific paper

We propose the notion of quasi-abelian third cohomology of crossed modules, generalizing Eilenberg and MacLane's abelian cohomology and Ospel's quasi-abelian cohomology, and 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. A criterion for these categories to be modular is given. We also describe the quasi-triangular quasi-Hopf algebras underlying these categories.

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