Contramodules for algebraic groups: the existence of mock projectives
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914283801018368 |
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| author | Johnston, Dylan |
| author_facet | Johnston, Dylan |
| contents | Let $G$ be an affine algebraic group over an algebraically closed field of positive characteristic. Recent work of Hardesty, Nakano, and Sobaje gives necessary and sufficient conditions for the existence of so-called mock injective $G$-modules, that is, modules which are injective upon restriction to all Frobenius kernels of $G$. In this paper, we give analogous results for contramodules, including showing that the same necessary and sufficient conditions on $G$ guarantee the existence of mock-projective contramodules. In order to do this we first develop contramodule analogs to many well-known (co)module constructions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16618 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Contramodules for algebraic groups: the existence of mock projectives Johnston, Dylan Representation Theory 20G05 (Primary), 18G05 (Secondary) Let $G$ be an affine algebraic group over an algebraically closed field of positive characteristic. Recent work of Hardesty, Nakano, and Sobaje gives necessary and sufficient conditions for the existence of so-called mock injective $G$-modules, that is, modules which are injective upon restriction to all Frobenius kernels of $G$. In this paper, we give analogous results for contramodules, including showing that the same necessary and sufficient conditions on $G$ guarantee the existence of mock-projective contramodules. In order to do this we first develop contramodule analogs to many well-known (co)module constructions. |
| title | Contramodules for algebraic groups: the existence of mock projectives |
| topic | Representation Theory 20G05 (Primary), 18G05 (Secondary) |
| url | https://arxiv.org/abs/2404.16618 |