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arXiv · 2304.05500

Rigidity for von Neumann algebras of graph product groups II. Superrigidity results

Ionut Chifan·Michael Davis·Daniel Drimbe
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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.

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Ionut Chifan, Michael Davis, Daniel Drimbe. 2023-04-11. Rigidity for von Neumann algebras of graph product groups II. Superrigidity results. https://arxiv.org/abs/2304.05500

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