Rigidity for von Neumann algebras of graph product groups. I. Structure of automorphisms
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908386656780288 |
|---|---|
| author | Chifan, Ionut Davis, Michael Drimbe, Daniel |
| author_facet | Chifan, Ionut Davis, Michael Drimbe, Daniel |
| contents | In this paper we study various rigidity aspects of the von Neumann algebra $L(Γ)$ where $Γ$ 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}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_12996 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Rigidity for von Neumann algebras of graph product groups. I. Structure of automorphisms Chifan, Ionut Davis, Michael Drimbe, Daniel Operator Algebras Group Theory In this paper we study various rigidity aspects of the von Neumann algebra $L(Γ)$ where $Γ$ 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}. |
| title | Rigidity for von Neumann algebras of graph product groups. I. Structure of automorphisms |
| topic | Operator Algebras Group Theory |
| url | https://arxiv.org/abs/2209.12996 |