Mathematics – Quantum Algebra
Scientific paper
2007-05-04
Comm. Math. Phys. 279 (2008), 845-872.
Mathematics
Quantum Algebra
26 pages; several comments and references added
Scientific paper
10.1007/s00220-008-0441-5
We classify Lagrangian subcategories of the representation category of a twisted quantum double of a finite group. In view of results of 0704.0195v2 this gives a complete description of all braided tensor equivalent pairs of twisted quantum doubles of finite groups. We also establish a canonical bijection between Lagrangian subcategories of the representation category of a twisted quantum double of a finite group G and module categories over the category of twisted G-graded vector spaces such that the dual tensor category is pointed. This can be viewed as a quantum version of V. Drinfeld's characterization of homogeneous spaces of a Poisson-Lie group in terms of Lagrangian subalgebras of the double of its Lie bialgebra. As a consequence, we obtain that two group-theoretical fusion categories are weakly Morita equivalent if and only if their centers are equivalent as braided tensor categories.
Naidu Deepak
Nikshych Dmitri
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