论文标题
$ {\ rm sl} _2（r）$的二分法属性 - 简短说明
The dichotomy property of ${\rm SL}_2(R)$-A short note
论文作者
论文摘要
Polterovich，Shalom和Shem-TOV最近发表的一篇论文表明，算术雪佛莉群体上的非二散的，共轭不变的规范会导致非常有限的拓扑结构。也就是说，这些拓扑始终具有大量的规范完成。在本说明中，我们绘制一个参数，表明这也适用于$ {\ rm sl} _2（r）$ for $ r $ a $ a ring a Ring a Ring a Ring a Ring a Ring tangebraic Integers具有无限的单位。
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.
