Free products and rescalings involving non-separable abelian von Neumann algebras
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866929712101588992 |
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| author | Dykema, Ken Zhao, Junchen |
| author_facet | Dykema, Ken Zhao, Junchen |
| contents | For a self-symmetric tracial von Neumann algebra $A$, we study rescalings of $A^{*n} * L\mathbb{F}_r$ for $n \in \mathbb{N}$ and $r \in (1, \infty]$ and use them to obtain an interpolation $\mathcal{F}_{s,r}(A)$ for all real numbers $s>0$ and $1-s < r \leq \infty$. We get formulas for their free products, and free products with finite-dimensional or hyperfinite von Neumann algebras. In particular, for any such $A$, we can compute compressions $(A^{*n})^t$ for $0<t<1$, and the Murray-von Neumann fundamental group of $A^{*\infty}$. When $A$ is also non-separable and abelian, this answers two questions in Section 4.3 of recent work of Boutonnet-Drimbe-Ioana-Popa. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08595 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Free products and rescalings involving non-separable abelian von Neumann algebras Dykema, Ken Zhao, Junchen Operator Algebras For a self-symmetric tracial von Neumann algebra $A$, we study rescalings of $A^{*n} * L\mathbb{F}_r$ for $n \in \mathbb{N}$ and $r \in (1, \infty]$ and use them to obtain an interpolation $\mathcal{F}_{s,r}(A)$ for all real numbers $s>0$ and $1-s < r \leq \infty$. We get formulas for their free products, and free products with finite-dimensional or hyperfinite von Neumann algebras. In particular, for any such $A$, we can compute compressions $(A^{*n})^t$ for $0<t<1$, and the Murray-von Neumann fundamental group of $A^{*\infty}$. When $A$ is also non-separable and abelian, this answers two questions in Section 4.3 of recent work of Boutonnet-Drimbe-Ioana-Popa. |
| title | Free products and rescalings involving non-separable abelian von Neumann algebras |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2502.08595 |