Amenable absorption in von Neumann algebras of hyperbolic groups

Juan Felipe Ariza Mejia; Ionut Chifan; Adriana Fernandez Quero; Adrian Ioana

doi:10.48550/arxiv.2606.10105

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Amenable absorption in von Neumann algebras of hyperbolic groups

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Amenable absorption in von Neumann algebras of hyperbolic groups

Juan Felipe Ariza Mejia, Ionut Chifan, Adriana Fernandez Quero and Adrian Ioana

ArXiv.org

Cornell University

06/08/2026

DOI: 10.48550/arxiv.2606.10105

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Preprint (Author's original) This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

We prove that the von Neumann algebra\cL{(}{G}{)}associated with any hyperbolic groupGsatisfies the following amenable absorption property: for any infinite maximal amenable subgroupH ≤ Gand any amenable von Neumann subalgebra𝓠 ⊂ \cL{(}{G}{)}with diffuse intersection with\cL{(}{H}{)} , one must have𝓠 ⊂ \cL{(}{H}{)} . This strengthens a result of Boutonnet and Carderi 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.

Mathematics - Operator Algebras

Details

Title: Subtitle: Amenable absorption in von Neumann algebras of hyperbolic groups
Creators: Juan Felipe Ariza Mejia
Ionut Chifan
Adriana Fernandez Quero
Adrian Ioana
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2606.10105
ISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 06/08/2026
Academic Unit: Mathematics
Record Identifier: 9985172994802771

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