A Tits alternative for $\mathbb{R}$-buildings of type $\tilde{A}_2$
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916470987948032 |
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| author | Bars, Corentin Le Lécureux, Jean Schillewaert, Jeroen |
| author_facet | Bars, Corentin Le Lécureux, Jean Schillewaert, Jeroen |
| contents | Let $G$ be a group with a non-elementary action on a (not necessarily discrete) $\tilde{A}_2$-buildings. We prove that, given a random walk on $G$, isometries in $G$ are strongly regular hyperbolic with high probability. As a consequence, we prove a Tits alternative for $G$, as well as a local-to-global fixed point result. We also prove that isometries of (not necessarily complete) $\mathbb{R}$-buildings are semi-simple. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04250 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Tits alternative for $\mathbb{R}$-buildings of type $\tilde{A}_2$ Bars, Corentin Le Lécureux, Jean Schillewaert, Jeroen Group Theory 20F65 (Primary) 20E42, 60G50 (Secondary) Let $G$ be a group with a non-elementary action on a (not necessarily discrete) $\tilde{A}_2$-buildings. We prove that, given a random walk on $G$, isometries in $G$ are strongly regular hyperbolic with high probability. As a consequence, we prove a Tits alternative for $G$, as well as a local-to-global fixed point result. We also prove that isometries of (not necessarily complete) $\mathbb{R}$-buildings are semi-simple. |
| title | A Tits alternative for $\mathbb{R}$-buildings of type $\tilde{A}_2$ |
| topic | Group Theory 20F65 (Primary) 20E42, 60G50 (Secondary) |
| url | https://arxiv.org/abs/2411.04250 |