Clifford theory for graded fusion categories


We develop a categorical analogue of Clifford theory for strongly graded rings over graded fusion categories. We describe module categories over a fusion category $\mathcal{C}$ graded by a group $G$ as induced from module categories over fusion subcategories associated with the subgroups of $G$. We define invariant $\mathcal{C}_e$-module categories and extensions of $\mathcal{C}_e$ -module categories. The construction of module categories over $\mathcal{C}$ is reduced to determining invariant module categories for subgroups of $G$ and the indecomposable extensions of these module categories. We associate a $G$-crossed product fusion category to each $G$-invariant $\mathcal{C}_e$ -module category and give a criterion for a graded fusion category to be a group-theoretical fusion category. We give necessary and sufficient conditions for an indecomposable module category to be extendable.

Israel J. Math. 192 (2012), no. 2, 841–867.
César Galindo
Associate Professor of Mathematics

My research interests include representation theory, category theory and their applications to Mathematical-Physics.