Group cohomology and gauge equivalence of some twisted quantum doubles (Q2716146)

The authors study the following question: Given two finite groups, each with a normalized 3-cocyle, when are the module categories of their twisted quantum doubles equivalent as braided monoidal categories?NEWLINENEWLINENEWLINEThis question of `multiplicative Morita equivalence' arises from the study of vertex operator algebras, but the notion is applicable, and looks to be interesting, in a much wider context. NEWLINENEWLINENEWLINEThe paper draws on a wide range of algebra developed over the past fifty years and provides techniques and results which give rise to a method for tackling the question in some generality. The authors also give complete answers for certain classes of groups.