Examples of W$^*$ and C$^*$-superrigid product groups
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910012898541568 |
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| author | Curda, Jakub Drimbe, Daniel |
| author_facet | Curda, Jakub Drimbe, Daniel |
| contents | We provide a new large class $\mathcal C_{AFP}$ of amalgamated free product groups for which the product rigidity result from [CdSS15] holds: if $G_1,\dots,G_n\in\mathcal C_{AFP}$ and $H$ is any group such that $L(G_1\times\dots\times G_n)\cong L(H)$, then there exists a product decomposition $H=H_1\times\dots\times H_n$ such that $L(H_i)$ is stably isomorphic to $L(G_i)$, for any $1\leq i\leq n$. The class $\mathcal C_{AFP}$ contains $W^*$ and $C^*$-superrigid groups from [CD-AD20]. Consequently, we obtain examples of product groups that are both $W^*$ and $C^*$-superrigid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_05618 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Examples of W$^*$ and C$^*$-superrigid product groups Curda, Jakub Drimbe, Daniel Operator Algebras We provide a new large class $\mathcal C_{AFP}$ of amalgamated free product groups for which the product rigidity result from [CdSS15] holds: if $G_1,\dots,G_n\in\mathcal C_{AFP}$ and $H$ is any group such that $L(G_1\times\dots\times G_n)\cong L(H)$, then there exists a product decomposition $H=H_1\times\dots\times H_n$ such that $L(H_i)$ is stably isomorphic to $L(G_i)$, for any $1\leq i\leq n$. The class $\mathcal C_{AFP}$ contains $W^*$ and $C^*$-superrigid groups from [CD-AD20]. Consequently, we obtain examples of product groups that are both $W^*$ and $C^*$-superrigid. |
| title | Examples of W$^*$ and C$^*$-superrigid product groups |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2602.05618 |