Rigidity for von Neumann algebras of graph product groups. I. Structure of automorphisms

Ionuţ Chifan; Michael Davis; Daniel Drimbe

doi:10.48550/arXiv.2209.12996

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Rigidity for von Neumann algebras of graph product groups. I. Structure of automorphisms

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Rigidity for von Neumann algebras of graph product groups. I. Structure of automorphisms

Ionuţ Chifan, Michael Davis and Daniel Drimbe

ArXiv.org

09/26/2022

DOI: 10.48550/arXiv.2209.12996

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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

In this paper we study various rigidity aspects of the von Neumann algebra $L(\Gamma)$ where $\Gamma$ is a graph product group \cite{Gr90} whose underlying graph is a certain cycle of cliques and the vertex groups are the wreath-like product property (T) groups introduced recently in \cite{CIOS21}. Using an approach that combines methods from Popa's deformation/rigidity theory with new techniques pertaining to graph product algebras, we describe all symmetries of these von Neumann algebras and reduced C$^*$-algebras by establishing formulas in the spirit of Genevois and Martin's results on automorphisms of graph product groups \cite{GM19}.

Details

Title: Subtitle: Rigidity for von Neumann algebras of graph product groups. I. Structure of automorphisms
Creators: Ionuţ Chifan
Michael Davis
Daniel Drimbe
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arXiv.2209.12996
ISSN: 2331-8422
Language: English
Date posted: 09/26/2022
Academic Unit: Mathematics
Record Identifier: 9984297659902771

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