On Relative Biexactness of Amalgamated Free 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_ | 1866913994837590016 |
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| author | Toyosawa, Kai Yang, Zhiyuan |
| author_facet | Toyosawa, Kai Yang, Zhiyuan |
| contents | Given weakly exact tracial von Neumann algebras $M_{1}, M_{2}$ with a common injective amalgam $B$, we prove that the amalgamated free product $M_{1}\overline{*}_{B}M_{2}$ is biexact relative to $\{M_{1},M_{2}\}$. In the case where $ M_1 $ and $M_2$ are injective, we further show that $M_{1}\overline{*}_{B}M_{2}$ is biexact relative to the amalgam $B$, and if $B$ is mixing in each of $M_1$ and $M_2$, $M_{1}\overline{*}_{B}M_{2}$ itself is biexact. As applications, we derive structural decomposition results and subalgebra absorption theorems for amalgamated free product von Neumann algebras, extending those previously known in the group case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_19508 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Relative Biexactness of Amalgamated Free Product von Neumann Algebras Toyosawa, Kai Yang, Zhiyuan Operator Algebras Given weakly exact tracial von Neumann algebras $M_{1}, M_{2}$ with a common injective amalgam $B$, we prove that the amalgamated free product $M_{1}\overline{*}_{B}M_{2}$ is biexact relative to $\{M_{1},M_{2}\}$. In the case where $ M_1 $ and $M_2$ are injective, we further show that $M_{1}\overline{*}_{B}M_{2}$ is biexact relative to the amalgam $B$, and if $B$ is mixing in each of $M_1$ and $M_2$, $M_{1}\overline{*}_{B}M_{2}$ itself is biexact. As applications, we derive structural decomposition results and subalgebra absorption theorems for amalgamated free product von Neumann algebras, extending those previously known in the group case. |
| title | On Relative Biexactness of Amalgamated Free Product von Neumann Algebras |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2505.19508 |