Preprint
Rigidity for von Neumann algebras of graph product groups II. Superrigidity results
ArXiv.org
04/11/2023
DOI: 10.48550/arxiv.2304.05500
Abstract
In \cite{CDD22} we investigated the structure of $\ast$-isomorphisms between
von Neumann algebras $L(\Gamma)$ associated with graph product groups $\Gamma$
of flower-shaped graphs and property (T) wreath-like product vertex groups as
in \cite{CIOS21}. In this follow-up we continue the structural study of these
algebras by establishing that these graph product groups $\Gamma$ are entirely
recognizable from the category of all von Neumann algebras arising from an
arbitrary non-trivial graph product group with infinite vertex groups. A
sharper $C^*$-algebraic version of this statement is also obtained. In the
process of proving these results we also extend the main $W^*$-superrigidity
result from \cite{CIOS21} to direct products of property (T) wreath-like
product groups.
Details
- Title: Subtitle
- Rigidity for von Neumann algebras of graph product groups II. Superrigidity results
- Creators
- Ionut ChifanMichael DavisDaniel Drimbe
- Resource Type
- Preprint
- Publication Details
- ArXiv.org
- DOI
- 10.48550/arxiv.2304.05500
- ISSN
- 2331-8422
- Language
- English
- Date posted
- 04/11/2023
- Academic Unit
- Mathematics
- Record Identifier
- 9984388754702771
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