论文标题
$ c^*$ - 相称的子组的不可约性
$C^*$-irreducibility of commensurated subgroups
论文作者
论文摘要
给定一个组$γ$的相称的子组$λ$，我们完全表征当包含$λ\ leqγ$为$ c^*$ - 不可约 - 不可约 - 并提供了此类包含的新示例。特别是，我们获得了$ \ rm {psl}（n，\ m \ m \ m mathbb {z}）\ leq \ rm {pgl}（n，n，\ mathbb {q}）$ is $ c^*$ - 不可用$ n \ in \ nathbb {n} $ comply in prippt in \ n offers in prippt its complation in $ c^$ c^$ - $ c^*$ - 不可约。我们使用的主要成分是一个事实是，在其Furstenberg边界上，相称的子组$λ\leqγ$的作用可以以独特的方式扩展到$ \partial_fλ$上的$γ$的独特方式。最后，我们还研究了该组的通用最小近端空间的此扩展结果的对应物。
Given a commensurated subgroup $Λ$ of a group $Γ$, we completely characterize when the inclusion $Λ\leq Γ$ is $C^*$-irreducible and provide new examples of such inclusions. In particular, we obtain that $\rm{PSL}(n,\mathbb{Z})\leq\rm{PGL}(n,\mathbb{Q})$ is $C^*$-irreducible for any $n\in \mathbb{N}$, and that the inclusion of a $C^*$-simple group into its abstract commensurator is $C^*$-irreducible. The main ingredient that we use is the fact that the action of a commensurated subgroup $Λ\leqΓ$ on its Furstenberg boundary $\partial_FΛ$ can be extended in a unique way to an action of $Γ$ on $\partial_FΛ$. Finally, we also investigate the counterpart of this extension result for the universal minimal proximal space of a group.
