局部紧凑群的严格外作用:超越全因子情况

Basile Morando
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引用次数: 0

摘要

我们证明,给定局部紧凑群$G$在因子$M$上的连续作用$\alpha$,相对换元$M'\cap(M\rtimes_{\alpha} G)$ 包含在$M\rtimes_{\alpha} H$中,其中$H$是无谱间隙作用的元素子群。作为一个推论,我们通过证明如果 $M$ 是半无限的,并且 $\alpha_g$ 对于所有 $gneq 1$ 都不近似,那么 $M'\cap (M\rtimes_{\alpha} G)=\mathbb{C}$ 回答了 Marrakchi 和 Vaes 的一个问题。
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Strictly outer actions of locally compact groups: beyond the full factor case
We show that, given a continuous action $\alpha$ of a locally compact group $G$ on a factor $M$, the relative commutant $M'\cap(M\rtimes_{\alpha} G)$ is contained in $M\rtimes_{\alpha} H$ where $H$ is the subgroup of elements acting without spectral gap. As a corollary, we answer a question of Marrakchi and Vaes by showing that if $M$ is semifinite and $\alpha_g$ is not approximately inner for all $g\neq 1$, then $M'\cap (M\rtimes_{\alpha} G)=\mathbb{C}$.
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