分段强邻近作用、自由边界和Neretin群
Piecewise strongly proximal actions, free boundaries and the Neretin groups
摘要：
局部紧群$G$的闭子群$H$是有界的，如果$H$的共轭类在$G$的Chabauty空间中的闭包不包含平凡子群.建立了一个关于全不连通的局部紧群$G$在紧空间$X$上作用的动力学判据，保证了$G$中没有相对顺从的子群被限制.这个性质等价于$G$在其Furstenberg边界上的作用是自由的。我们的标准适用于Neretin组。我们推出每个Neretin群有两个不等价的不可约酉表示是弱等价的。这意味着Neretin群不是I型的，从而回答了Y的问题。奈瑞汀
英文摘要：
A closed subgroup $H$ of a locally compact group $G$ is confined if the closure of the conjugacy class of $H$ in the Chabauty space of $G$ does not contain the trivial subgroup. We establish a dynamical criterion on the action of a totally disconnected locally compact group $G$ on a compact space $X$ ensuring that no relatively amenable subgroup of $G$ can be confined. This property is equivalent to the fact that the action of $G$ on its Furstenberg boundary is free. Our criterion applies to the Neretin groups. We deduce that each Neretin group has two inequivalent irreducible unitary representations that are weakly equivalent. This implies that the Neretin groups are not of type I, thereby answering a question of Y.~Neretin.
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