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arXiv · 2309.10494

On the amenable subalgebras of group von Neumann algebras

Tattwamasi Amrutam·Yair Hartman·Hanna Oppelmayer
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Abstract

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.

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BibTeXRIS

Tattwamasi Amrutam, Yair Hartman, Hanna Oppelmayer. 2023-09-19. On the amenable subalgebras of group von Neumann algebras. https://doi.org/10.1016/j.jfa.2024.110718

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