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arXiv · 2606.10105

Amenable absorption in von Neumann algebras of hyperbolic groups

Juan Felipe Ariza Mejia·Ionut Chifan·Adriana Fernandez Quero·Adrian Ioana
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Abstract

We prove that the von Neumann algebra $\cL(G)$ associated with any hyperbolic group $G$ satisfies the following \emph{amenable absorption property}: for any infinite maximal amenable subgroup $H \leqslant G$ and any amenable von Neumann subalgebra $\mathcal{Q} \subset \cL(G)$ with diffuse intersection with $\cL(H)$, one must have $\mathcal{Q} \subset \cL(H)$. This strengthens a result of Boutonnet and Carderi \cite{BC2}. We also establish similar amenable absorption results for the broader class of acylindrically hyperbolic groups, including relatively hyperbolic groups, mapping class groups, and limit groups.

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Juan Felipe Ariza Mejia, Ionut Chifan, Adriana Fernandez Quero, Adrian Ioana. 2026-06-08. Amenable absorption in von Neumann algebras of hyperbolic groups. https://arxiv.org/abs/2606.10105

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