On finite group scheme-theoretical categories, II
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914032134389760 |
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| author | Gelaki, Shlomo Sanmarco, Guillermo |
| author_facet | Gelaki, Shlomo Sanmarco, Guillermo |
| contents | Let $\mathcal{C}:=\mathcal{C}(G,ω,H,ψ)$ be a finite group scheme-theoretical category over an algebraically closed field of characteristic $p\ge 0$ as defined by the first author. For any indecomposable exact module category over $\mathcal{C}$, 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 of $G$. This upgrades a result of Ostrik for group-theoretical fusion categories in characteristic $0$, and generalizes our previous work for the case $ω=1$. As a byproduct, we describe the simples and indecomposable projectives of $\mathcal{C}$. Finally, we apply our results to describe the blocks of the center of ${\rm Coh}(G,ω)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_08785 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On finite group scheme-theoretical categories, II Gelaki, Shlomo Sanmarco, Guillermo Representation Theory 18M20, 16T05, 17B37 Let $\mathcal{C}:=\mathcal{C}(G,ω,H,ψ)$ be a finite group scheme-theoretical category over an algebraically closed field of characteristic $p\ge 0$ as defined by the first author. For any indecomposable exact module category over $\mathcal{C}$, 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 of $G$. This upgrades a result of Ostrik for group-theoretical fusion categories in characteristic $0$, and generalizes our previous work for the case $ω=1$. As a byproduct, we describe the simples and indecomposable projectives of $\mathcal{C}$. Finally, we apply our results to describe the blocks of the center of ${\rm Coh}(G,ω)$. |
| title | On finite group scheme-theoretical categories, II |
| topic | Representation Theory 18M20, 16T05, 17B37 |
| url | https://arxiv.org/abs/2403.08785 |