Equivariant modular categories via Dijkgraaf–Witten theory

Abstract

Based on a weak action of a finite group $J$ on a finite group $G$, we present a geometric construction of $J$-equivariant Dijkgraaf–Witten theory as an extended topological field theory. The construction yields an explicitly accessible class of equivariant modular tensor categories. For the action of a group $J$ on a group $G$, the category is described as the representation category of a $J$-ribbon algebra that generalizes the Drinfel’d double of the finite group $G$.