Algebraic Structures in Group-theoretical Fusion Categories

It was shown by Ostrik (Int. Math. Res. Not. 2003(27), 1507–1520 2003) and Natale (SIGMA Symmetry Integrability Geom. Methods Appl. 13, 042 2017) that a collection of twisted group algebras in pointed fusion category serve as explicit Morita equivalence class representatives indecomposable, separable such categories. We generalize this result constructing group-theoretical This is achieved providing the free functor Φ from to bimodules original with (Frobenius) monoidal structure. Our interest are then constructed image under Φ. also show admit structure Frobenius category, consequence, our category. They enjoy several good algebraic properties.