Fusion subcategories of representation categories of twisted quantum doubles of finite groups

By D. Venku Naidu, D. Nikshych, S. Witherspoon. 2008

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We describe all fusion subcategories of the representation category of a twisted quantum double of a finite group. In view of the fact that every group-theoretical braided fusion category can be embedded into a representation category of a twisted quantum double of a finite group, this gives a complete description of all group-theoretical braided fusion categories. We describe the lattice and give formulas for some invariants of the fusion subcategories of representation category of a twisted quantum double of a finite group. We also give a characterization of group-theoretical braided fusion categories as equivariantizations of pointed categories.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/aba60b2426c72707d371d3f1616e80b368fac239