Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.16162 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917218133999616 |
|---|---|
| author | Sercombe, Damian |
| author_facet | Sercombe, Damian |
| contents | We introduce a unified theory of Cartan subgroups and maximal toroids - defined as connected multiplicative type subgroups that are maximal amongst all such subgroups - which holds for all affine algebraic groups over a field, regardless of smoothness. For instance we show that maximal toroids always exist, that they are invariant under base change, and that they are in natural 1-1 correspondence with Cartan subgroups. Our results generalise known results for Cartan subgroups and maximal tori of smooth affine algebraic groups, as well as their analogues for restricted Lie algebras. We conclude with some applications to, and a brief discussion of, some generation problems for algebraic groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16162 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Maximal toroids and Cartan subgroups of algebraic groups Sercombe, Damian Group Theory 20G15 (Primary) 20G07 (Secondary) We introduce a unified theory of Cartan subgroups and maximal toroids - defined as connected multiplicative type subgroups that are maximal amongst all such subgroups - which holds for all affine algebraic groups over a field, regardless of smoothness. For instance we show that maximal toroids always exist, that they are invariant under base change, and that they are in natural 1-1 correspondence with Cartan subgroups. Our results generalise known results for Cartan subgroups and maximal tori of smooth affine algebraic groups, as well as their analogues for restricted Lie algebras. We conclude with some applications to, and a brief discussion of, some generation problems for algebraic groups. |
| title | Maximal toroids and Cartan subgroups of algebraic groups |
| topic | Group Theory 20G15 (Primary) 20G07 (Secondary) |
| url | https://arxiv.org/abs/2601.16162 |