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Fusion in the Extended Verlinde Algebra

Vincent Graziano
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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 $\mathcal{U}_{q}(\mathfrak{sl}_{2})$.

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Vincent Graziano. 2006-07-30. Fusion in the Extended Verlinde Algebra. https://arxiv.org/abs/math/0607786

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