圈积II $_1$因子的刚度结果
Rigidity results for wreath product II$_1$ factors
摘要：
我们考虑形式为$M=\bar{\bigotimes}_{G}N\rtimes G$的II $_1$因子，其中i）$N$是非超有限II $_1$因子，$G$是ICC顺从群，或者ii）$N$是弱刚性II $_1$因子，$G$是ICC群，其中$G$通过Bernoulli移位作用于$\bar{\bigotimes}_{G}N$。我们证明了两个这样的因子的同构蕴涵相应的伯努利移位作用的上循环共轭。特别地，作用的群是同构的。因此，我们可以区分某些类的群冯诺依曼代数相关的圈积群。
英文摘要：
We consider II$_1$ factors of the form $M=\bar{\bigotimes}_{G}N\rtimes G$, where either i) $N$ is a non-hyperfinite II$_1$ factor and $G$ is an ICC amenable group or ii) $N$ is a weakly rigid II$_1$ factor and $G$ is ICC group and where $G$ acts on $\bar{\bigotimes}_{G}N$ by Bernoulli shifts. We prove that isomorphism of two such factors implies cocycle conjugacy of the corresponding Bernoulli shift actions. In particular, the groups acting are isomorphic. As a consequence, we can distinguish between certain classes of group von Neumann algebras associated to wreath product groups.
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