Strongly solid group factors which are not interpolated free group factors
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arXiv
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| Format: | Preprint |
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2009
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| _version_ | 1866913943629332480 |
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| author | Houdayer, Cyril |
| author_facet | Houdayer, Cyril |
| contents | We give examples of non-amenable ICC groups $Γ$ with the Haagerup property, weakly amenable with constant $Λ_{\cb}(Γ) = 1$, for which we show that the associated ${\rm II_1}$ factors $L(Γ)$ are strongly solid, i.e. the normalizer of any diffuse amenable subalgebra $P \subset L(Γ)$ generates an amenable von Neumann algebra. Nevertheless, for these examples of groups $Γ$, $L(Γ)$ is not isomorphic to any interpolated free group factor $L(\F_t)$, for $1 < t \leq \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_0901_3866 |
| institution | arXiv |
| publishDate | 2009 |
| record_format | arxiv |
| spellingShingle | Strongly solid group factors which are not interpolated free group factors Houdayer, Cyril Operator Algebras Group Theory 46L10, 46L54 (Primary) 22D25, 37A20 (Secondary) We give examples of non-amenable ICC groups $Γ$ with the Haagerup property, weakly amenable with constant $Λ_{\cb}(Γ) = 1$, for which we show that the associated ${\rm II_1}$ factors $L(Γ)$ are strongly solid, i.e. the normalizer of any diffuse amenable subalgebra $P \subset L(Γ)$ generates an amenable von Neumann algebra. Nevertheless, for these examples of groups $Γ$, $L(Γ)$ is not isomorphic to any interpolated free group factor $L(\F_t)$, for $1 < t \leq \infty$. |
| title | Strongly solid group factors which are not interpolated free group factors |
| topic | Operator Algebras Group Theory 46L10, 46L54 (Primary) 22D25, 37A20 (Secondary) |
| url | https://arxiv.org/abs/0901.3866 |