Strictly outer actions of locally compact groups: Beyond the full factor case
Year: 2025
Type: article
Abstract: We show that, given a continuous action $α$ of a locally compact group $G$ on a factor $M$, the relative commutant $M'\cap(M\rtimes_α G)$ is contained in $M\rtimes_α H$ 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 $α_g$ is not approximately inner for all $g\neq 1$, then $M'\cap (M\rtimes_α G)=\mathbb{C}$.
Source: Journal of Functional Analysis
Author: Basile Morando
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,250
OpenAlex ID: W4408108679