On the amenable subalgebras of group von Neumann algebras

Autor:	Amrutam, Tattwamasi, Hartman, Yair, Oppelmayer, Hanna
Rok vydání:	2023
Předmět:	Mathematics - Operator Algebras Mathematics - Dynamical Systems Mathematics - Functional Analysis Mathematics - Probability 46L10 (Primary) 22D25 47A35 (Secondary)
Zdroj:	Journal of Functional Analysis, 2024
Druh dokumentu:	Working Paper
DOI:	10.1016/j.jfa.2024.110718
Popis:	We approach the study of sub-von Neumann algebras of the group von Neumann algebra $L\Gamma$ for countable groups $\Gamma$ from a dynamical perspective. It is shown that $L(\Gamma)$ admits a maximal invariant amenable subalgebra. The notion of invariant probability measures (IRAs) on the space of sub-algebras is introduced, analogous to the concept of Invariant Random Subgroups. And it is shown that amenable IRAs are supported on the maximal amenable invariant sub-algebra. Comment: This final version will appear in the Journal of Functional Analysis
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2309.10494 Zobrazit plný text záznamu View this record from Arxiv