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- W4381551116 abstract "Let $mathscr {C}$ denote a finite group scheme-theoretical category over an algebraically closed field of characteristic $pge 0$ as introduced by the first author. For any indecomposable exact module category over $mathscr {C}$, we classify its simple objects and provide an expression for their projective covers, in terms of double cosets and projective representations of certain closed subgroup schemes, which upgrades a result by Ostrik for group-theoretical fusion categories. As a byproduct, we describe the simples and indecomposable projectives of $mathscr {C}$, and parametrize the Brauer-Piccard group of ${rm Coh}(G)$ for any finite connected group scheme $G$. Finally, we apply our results to describe the blocks of the center of ${rm Coh}(G)$, which is a group scheme-theoretical category." @default.
- W4381551116 created "2023-06-22" @default.
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- W4381551116 date "2023-06-16" @default.
- W4381551116 modified "2023-10-18" @default.
- W4381551116 title "On finite group scheme-theoretical categories" @default.
- W4381551116 doi "https://doi.org/10.48550/arxiv.2306.10205" @default.
- W4381551116 hasPublicationYear "2023" @default.
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