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arXiv · 2202.08319

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

Alexander Alois Trost
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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 ${\rm SL}_2(R)$ for $R$ a ring of algebraic integers with infinitely many units.

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Alexander Alois Trost. 2022-02-16. The dichotomy property of ${\rm SL}_2(R)$-A short note. https://arxiv.org/abs/2202.08319

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