462 research outputs found
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 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.Comment: Corollary 5.5 has been corrected. Accepted by Israel Journal of
Mathematic
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