Clifford theory for graded fusion categories
arXiv:1010.5283
Abstract
We develop a categorical analogue of Clifford theory for strongly graded rings over graded fusion categories. We describe module categories over a fusion category graded by a group as induced from module categories over fusion subcategories associated with the subgroups of . We define invariant $\C_e$-module categories and extensions of $\C_e$-module categories. The construction of module categories over $\C$ is reduced to determine invariant module categories for subgroups of and the indecomposable extensions of this modules categories. We associate a -crossed product fusion category to each -invariant $\C_e$-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 extended.
Corollary 5.5 has been corrected. Accepted by Israel Journal of Mathematics