Rigidity for von Neumann algebras of graph product groups II. Superrigidity results
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916769433649152 |
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| author | Chifan, Ionut Davis, Michael Drimbe, Daniel |
| author_facet | Chifan, Ionut Davis, Michael Drimbe, Daniel |
| contents | In \cite{CDD22} we investigated the structure of $\ast$-isomorphisms between von Neumann algebras $L(Γ)$ associated with graph product groups $Γ$ 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 $Γ$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_05500 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rigidity for von Neumann algebras of graph product groups II. Superrigidity results Chifan, Ionut Davis, Michael Drimbe, Daniel Operator Algebras Group Theory In \cite{CDD22} we investigated the structure of $\ast$-isomorphisms between von Neumann algebras $L(Γ)$ associated with graph product groups $Γ$ 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 $Γ$ 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. |
| title | Rigidity for von Neumann algebras of graph product groups II. Superrigidity results |
| topic | Operator Algebras Group Theory |
| url | https://arxiv.org/abs/2304.05500 |