Reidemeister numbers for arithmetic Borel subgroups in type A
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912885088714752 |
|---|---|
| author | de Araujo, Paula Macedo Lins Rego, Yuri Santos |
| author_facet | de Araujo, Paula Macedo Lins Rego, Yuri Santos |
| contents | The Reidemeister number $R(φ)$ of a group automorphism $φ\in \mathrm{Aut}(G)$ encodes the number of orbits of the $φ$-twisted conjugation action of $G$ on itself, and the Reidemeister spectrum of $G$ is defined as the set of Reidemeister numbers of all of its automorphisms. We obtain a sufficient criterion for some groups of triangular matrices over integral domains to have property $R_\infty$, which means that their Reidemeister spectrum equals $\{\infty\}$. Using this criterion, we show that Reidemeister numbers for certain soluble $S$-arithmetic groups behave differently from their linear algebraic counterparts -- contrasting with results of Steinberg, Bhunia, and Bose. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_02936 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Reidemeister numbers for arithmetic Borel subgroups in type A de Araujo, Paula Macedo Lins Rego, Yuri Santos Group Theory 20E36, 20F16, 20G30 The Reidemeister number $R(φ)$ of a group automorphism $φ\in \mathrm{Aut}(G)$ encodes the number of orbits of the $φ$-twisted conjugation action of $G$ on itself, and the Reidemeister spectrum of $G$ is defined as the set of Reidemeister numbers of all of its automorphisms. We obtain a sufficient criterion for some groups of triangular matrices over integral domains to have property $R_\infty$, which means that their Reidemeister spectrum equals $\{\infty\}$. Using this criterion, we show that Reidemeister numbers for certain soluble $S$-arithmetic groups behave differently from their linear algebraic counterparts -- contrasting with results of Steinberg, Bhunia, and Bose. |
| title | Reidemeister numbers for arithmetic Borel subgroups in type A |
| topic | Group Theory 20E36, 20F16, 20G30 |
| url | https://arxiv.org/abs/2306.02936 |