The atoms of graph product von Neumann algebras
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910998998286336 |
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| author | Charlesworth, Ian Jekel, David |
| author_facet | Charlesworth, Ian Jekel, David |
| contents | We completely classify the atomic summands in a graph product $(M,φ) = *_{v \in \mathcal{G}} (M_v,φ_v)$ of von Neumann algebras with faithful normal states. Each type I factor summand $(N,ψ)$ is a tensor product of type I factor summands $(N_v,ψ_v)$ in the individual algebras. The existence of such a summand and its weight in the direct sum can be determined from the $(N_v,ψ_v)$'s using explicit polynomials associated to the graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_09000 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The atoms of graph product von Neumann algebras Charlesworth, Ian Jekel, David Operator Algebras Probability 46L10, 46L54, 05C25, 05C31 We completely classify the atomic summands in a graph product $(M,φ) = *_{v \in \mathcal{G}} (M_v,φ_v)$ of von Neumann algebras with faithful normal states. Each type I factor summand $(N,ψ)$ is a tensor product of type I factor summands $(N_v,ψ_v)$ in the individual algebras. The existence of such a summand and its weight in the direct sum can be determined from the $(N_v,ψ_v)$'s using explicit polynomials associated to the graph. |
| title | The atoms of graph product von Neumann algebras |
| topic | Operator Algebras Probability 46L10, 46L54, 05C25, 05C31 |
| url | https://arxiv.org/abs/2506.09000 |