Algebra Commons^™

We establish braided tensor equivalences among module categories over the twisted quantum double of a finite group defined by an extension of a group H by an abelian group, with 3-cocycle inflated from a 3-cocycle on H. We also prove that the canonical ribbon structure of the module category of any twisted quantum double of a finite group is preserved by braided tensor equivalences. We give two main applications: first, if G is an extra-special 2-group of width at least 2, we show that the quantum double of G twisted by a 3-cocycle w is gauge equivalent to a twisted …

We exhibit an isomorphism between the fusion algebra of the quantum double of an extraspecial p-group, where p is an odd prime, and the fusion algebra of a twisted quantum double of an elementary abelian group of the same order.

Let D^ω(G) be the twisted quantum double of a finite group, G, where ω∈Z³(G,C∗). For each n∈N, there exists an ω such that D(G) and D^ω(E) have isomorphic fusion algebras, where G is an extraspecial 2-group with 2²ⁿ⁺¹ elements, and E is an elementary abelian group with |E|=|G|.