Invariant subalgebras of von Neumann algebras arising from negatively curved groups

Ionuţ Chifan; Sayan Das; Bin Sun

doi:10.1016/j.jfa.2023.110098

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Invariant subalgebras of von Neumann algebras arising from negatively curved groups

Journal article

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Invariant subalgebras of von Neumann algebras arising from negatively curved groups

Ionuţ Chifan, Sayan Das and Bin Sun

Journal of functional analysis, Vol.285(9), 110098

11/2023

DOI: 10.1016/j.jfa.2023.110098

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Abstract

Using an interplay between geometric methods in group theory and soft von Neuman algebraic techniques we prove that for any icc, acylindrically hyperbolic group Γ its von Neumann algebra L(Γ) satisfies the so-called ISR property: any von Neumann subalgebraN⊆L(Γ)that is normalized by all group elements in Γ is of the formN=L(Σ)for a normal subgroupΣ◁Γ. In particular, this applies to all groups Γ in each of the following classes: all icc (relatively) hyperbolic groups, most mapping class groups of surfaces, all outer automorphisms of free groups with at least three generators, most graph product groups arising from simple graphs without visual splitting, etc. This result answers positively an open question of Amrutam and Jiang from [2]. In the second part of the paper we obtain similar results for factors associated with groups that admit nontrivial (quasi)cohomology valued into various natural representations. In particular, we establish the ISR property for all icc, nonamenable groups that have positive first L2-Betti number and contain an infinite amenable subgroup.

Geometric group theory

Popa's deformation/rigidity theory

von Neumann algebras

Details

Title: Subtitle: Invariant subalgebras of von Neumann algebras arising from negatively curved groups
Creators: Ionuţ Chifan - Department of Mathematics, The University of Iowa, 14 MacLean Hall, Iowa City, IA 52242, USA
Sayan Das - Department of Mathematics, Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA
Bin Sun - University of Oxford
Resource Type: Journal article
Publication Details: Journal of functional analysis, Vol.285(9), 110098
Publisher: Elsevier Inc
DOI: 10.1016/j.jfa.2023.110098
ISSN: 0022-1236
eISSN: 1096-0783
Grant note: DOI: 10.13039/100008893, name: The University of Iowa; DOI: 10.13039/501100000769, name: University of Oxford; DOI: 10.13039/501100000781, name: European Research Council; DOI: 10.13039/501100007601, name: Horizon 2020, award: 850930; DOI: 10.13039/100000001, name: National Science Foundation, award: DMS-2154637, FRG-DMS-1854194
Language: English
Date published: 11/2023
Academic Unit: Mathematics
Record Identifier: 9984453331102771

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