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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2505.05179 |
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| _version_ | 1866908865752203264 |
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| author | Caspers, Martijn Chen, Enli |
| author_facet | Caspers, Martijn Chen, Enli |
| contents | In this paper, we show that for a graph $Γ$ from a class named H-rigid graphs, its subgraph ${\rm Int}(Γ)$, named the internal graph of $Γ$, is an isomorphism invariant of the graph product of hyperfinite II$_1$-factors $R_Γ$. In particular, we can classify $R_Γ$ for some typical types of graphs, such as lines, cyclic graphs and infinite regular trees. As an application, we also show that for two isomorphic graph products of hyperfinite II$_1$-factors over H-rigid graphs, the difference of the radius between the two graphs will not be larger than 1. Our proof is based on the recent resolution of the Peterson-Thom conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05179 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Internal graphs of graph products of hyperfinite II$_1$-factors Caspers, Martijn Chen, Enli Operator Algebras 47C15, 47B02 In this paper, we show that for a graph $Γ$ from a class named H-rigid graphs, its subgraph ${\rm Int}(Γ)$, named the internal graph of $Γ$, is an isomorphism invariant of the graph product of hyperfinite II$_1$-factors $R_Γ$. In particular, we can classify $R_Γ$ for some typical types of graphs, such as lines, cyclic graphs and infinite regular trees. As an application, we also show that for two isomorphic graph products of hyperfinite II$_1$-factors over H-rigid graphs, the difference of the radius between the two graphs will not be larger than 1. Our proof is based on the recent resolution of the Peterson-Thom conjecture. |
| title | Internal graphs of graph products of hyperfinite II$_1$-factors |
| topic | Operator Algebras 47C15, 47B02 |
| url | https://arxiv.org/abs/2505.05179 |