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

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

2008-09-30

arxiv.org/abs/0810.0032v2

Int. Math. Res. Not. (2009), no. 22, 4183-4219

Mathematics

Quantum Algebra

28 pages, Remarks 4.6 and 4.7 added at the suggestion of the referee

Scientific paper

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.

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