On some free products of von Neumann algebras which are free Araki-Woods factors
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arXiv
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| Format: | Preprint |
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2006
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| _version_ | 1866915393861320704 |
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| author | Houdayer, Cyril |
| author_facet | Houdayer, Cyril |
| contents | We prove that certain free products of factors of type ${\rm I}$ and other von Neumann algebras with respect to nontracial, almost periodic states are almost periodic free Araki-Woods factors. In particular, they have the free absorption property and Connes' Sd invariant completely classifies these free products. For example, for $λ, μ\in ]0, 1[$, we show that $$(M_2(\C), ω_λ) \ast (M_2(\C), ω_μ)$$ is isomorphic to the free Araki-Woods factor whose Sd invariant is the subgroup of $\R^*_+$ generated by $λ$ and $μ$. Our proofs are based on algebraic techniques and amalgamated free products. These results give some answers to questions of Dykema and Shlyakhtenko. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_math_0606271 |
| institution | arXiv |
| publishDate | 2006 |
| record_format | arxiv |
| spellingShingle | On some free products of von Neumann algebras which are free Araki-Woods factors Houdayer, Cyril Operator Algebras 46L10, 46L54 We prove that certain free products of factors of type ${\rm I}$ and other von Neumann algebras with respect to nontracial, almost periodic states are almost periodic free Araki-Woods factors. In particular, they have the free absorption property and Connes' Sd invariant completely classifies these free products. For example, for $λ, μ\in ]0, 1[$, we show that $$(M_2(\C), ω_λ) \ast (M_2(\C), ω_μ)$$ is isomorphic to the free Araki-Woods factor whose Sd invariant is the subgroup of $\R^*_+$ generated by $λ$ and $μ$. Our proofs are based on algebraic techniques and amalgamated free products. These results give some answers to questions of Dykema and Shlyakhtenko. |
| title | On some free products of von Neumann algebras which are free Araki-Woods factors |
| topic | Operator Algebras 46L10, 46L54 |
| url | https://arxiv.org/abs/math/0606271 |