Fusion in the Extended Verlinde Algebra

Abstract

In this paper we study modular $G$-equivariant fusion categories and their extended Verlinde algebras. We dicuss settings in which fusion rules are diagonalizable. In particular, when $G={\mathbb{Z}}_2$ we generalize the Verlinde formula. We discuss an important example at length: the type $D_{2m+2}$ quantum subgroup of the semisimple representations of ${\mathcal{U}}_q({\mathfrak{sl}}_2)$.

33 pages, 7 figures

References in corpus (3)

• Homotopy field theory in dimension 3 and crossed group-categories
• Group Cohomology and Gauge Equivalence of some Twisted Quantum Doubles
• On $G$--equivariant modular categories