English

The dichotomy property of ${\rm SL}_2(R)$-A short note

Group Theory 2022-02-18 v1

Abstract

A recent paper by Polterovich, Shalom and Shem-Tov has shown that non-discrete, conjugation invariant norms on arithmetic Chevalley groups of higher rank give rise to very restricted topologies. Namely, such topologies always have profinite norm-completions. In this note, we sketch an argument showing that this also holds for SL2(R){\rm SL}_2(R) for RR a ring of algebraic integers with infinitely many units.

Keywords

Cite

@article{arxiv.2202.08319,
  title  = {The dichotomy property of ${\rm SL}_2(R)$-A short note},
  author = {Alexander Alois Trost},
  journal= {arXiv preprint arXiv:2202.08319},
  year   = {2022}
}