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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.05192 |
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| _version_ | 1866916548923359232 |
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| author | Andrew, Naomi Conder, Matthew J. Markowitz, Ari Schillewaert, Jeroen |
| author_facet | Andrew, Naomi Conder, Matthew J. Markowitz, Ari Schillewaert, Jeroen |
| contents | Let $K$ be a non-archimedean local field. We show that discrete subgroups without 2-torsion in $\mathrm{PSL}_2(K)$ can always be lifted to $\mathrm{SL}_2(K)$, and provide examples (when $\mathrm{char}(K) \neq 2$) which cannot be lifted if either of these conditions is removed. We also briefly discuss lifting representations of groups into $\mathrm{PSL}_2(K)$ to $\mathrm{SL}_2(K)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05192 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lifting subgroups of $\mathrm{PSL}_2$ to $\mathrm{SL}_2$ over local fields Andrew, Naomi Conder, Matthew J. Markowitz, Ari Schillewaert, Jeroen Group Theory Number Theory 20G25 (Primary) 20E08 (Secondary) Let $K$ be a non-archimedean local field. We show that discrete subgroups without 2-torsion in $\mathrm{PSL}_2(K)$ can always be lifted to $\mathrm{SL}_2(K)$, and provide examples (when $\mathrm{char}(K) \neq 2$) which cannot be lifted if either of these conditions is removed. We also briefly discuss lifting representations of groups into $\mathrm{PSL}_2(K)$ to $\mathrm{SL}_2(K)$. |
| title | Lifting subgroups of $\mathrm{PSL}_2$ to $\mathrm{SL}_2$ over local fields |
| topic | Group Theory Number Theory 20G25 (Primary) 20E08 (Secondary) |
| url | https://arxiv.org/abs/2401.05192 |