Relative bi-exactness and structural results for graph-wreath product von Neumann algebras
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908788733247488 |
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| author | Hoshino, Taisuke |
| author_facet | Hoshino, Taisuke |
| contents | We study relative bi-exactness of graph product and graph-wreath product group von Neumann algebras. In particular, we obtain the relative bi-exactness for graph product von Neumann algebras $LH_Γ=\ast_{v,Γ} LH_v$ and graph-wreath product von Neumann algebras $L(H_Γ\rtimes G)=(\ast_{v,Γ} LH)\rtimes G$, assuming that the component groups are exact. We adopt the $C^{\ast}$-algebraic method of Ozawa for the proof. As an application, for a certain class of graph-wreath products, we establish the rigidity result for the quotient graph $G\backslashΓ$ under stable isomorphism. Furthermore, we obtain a new family of prime $\mathrm{II}_1$ factors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18185 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Relative bi-exactness and structural results for graph-wreath product von Neumann algebras Hoshino, Taisuke Operator Algebras We study relative bi-exactness of graph product and graph-wreath product group von Neumann algebras. In particular, we obtain the relative bi-exactness for graph product von Neumann algebras $LH_Γ=\ast_{v,Γ} LH_v$ and graph-wreath product von Neumann algebras $L(H_Γ\rtimes G)=(\ast_{v,Γ} LH)\rtimes G$, assuming that the component groups are exact. We adopt the $C^{\ast}$-algebraic method of Ozawa for the proof. As an application, for a certain class of graph-wreath products, we establish the rigidity result for the quotient graph $G\backslashΓ$ under stable isomorphism. Furthermore, we obtain a new family of prime $\mathrm{II}_1$ factors. |
| title | Relative bi-exactness and structural results for graph-wreath product von Neumann algebras |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2601.18185 |