Advances in Theoretical and Mathematical Physics
Volume 16 (2012)
Equivariant modular categories via Dijkgraaf–Witten theory
Pages: 289 – 358
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 $G$.