Unipotent normal subgroups of algebraic groups
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908780098224128 |
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| author | Sercombe, Damian |
| author_facet | Sercombe, Damian |
| contents | Let $G$ be an affine algebraic group scheme over a field $k$. We show there exists a unipotent normal subgroup of $G$ which contains all other such subgroups; we call it the restricted unipotent radical $\mathrm{Rad}_u(G)$ of $G$. We investigate some properties of $\mathrm{Rad}_u(G)$, and study those $G$ for which $\mathrm{Rad}_u(G)$ is trivial. In particular, we relate these notions to their well-known analogues for smooth connected affine $k$-groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12221 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unipotent normal subgroups of algebraic groups Sercombe, Damian Group Theory 20G15 (Primary) 20G07 (Secondary) Let $G$ be an affine algebraic group scheme over a field $k$. We show there exists a unipotent normal subgroup of $G$ which contains all other such subgroups; we call it the restricted unipotent radical $\mathrm{Rad}_u(G)$ of $G$. We investigate some properties of $\mathrm{Rad}_u(G)$, and study those $G$ for which $\mathrm{Rad}_u(G)$ is trivial. In particular, we relate these notions to their well-known analogues for smooth connected affine $k$-groups. |
| title | Unipotent normal subgroups of algebraic groups |
| topic | Group Theory 20G15 (Primary) 20G07 (Secondary) |
| url | https://arxiv.org/abs/2404.12221 |