Lifting subgroups of $\mathrm{PSL}_2$ to $\mathrm{SL}_2$ over local fields

Naomi Andrew; Matthew J. Conder; Ari Markowitz; Jeroen Schillewaert

Lifting subgroups of $\mathrm{PSL}_2$ to $\mathrm{SL}_2$ over local fields

Group Theory 2025-01-06 v2 Number Theory

Authors: Naomi Andrew , Matthew J. Conder , Ari Markowitz , Jeroen Schillewaert

Abstract

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 $\mathrm{SL}_2(K)$ .

Cite

@article{arxiv.2401.05192,
  title  = {Lifting subgroups of $\mathrm{PSL}_2$ to $\mathrm{SL}_2$ over local fields},
  author = {Naomi Andrew and Matthew J. Conder and Ari Markowitz and Jeroen Schillewaert},
  journal= {arXiv preprint arXiv:2401.05192},
  year   = {2025}
}

Comments

14 pages. v2: final version, to appear in Journal of Group Theory

Lifting subgroups of $\mathrm{PSL}_2$ to $\mathrm{SL}_2$ over local fields

Abstract

Cite

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