A family of isomorphic fusion algebras of twisted quantum doubles of finite groups (Q1867321)

Let \(G\) be an extraspecial 2-group with \(2^{2n+1}\) elements. It is proved that there exist an elementary abelian group \(E\) with \(|E|=|G|\), and \(\omega \in Z^3(E,{\mathbb C}^*)\), such that the quantum double \(D(G)\) and the twisted quantum double \(D^{\omega}(E)\) have isomorphic fusion algebras.