A class of ${\rm II_1}$ factors with an exotic abelian maximal amenable subalgebra
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arXiv
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| Format: | Preprint |
| Publié: |
2012
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| _version_ | 1866916845643104256 |
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| author | Houdayer, Cyril |
| author_facet | Houdayer, Cyril |
| contents | We show that for every mixing orthogonal representation $π: \Z \to \mathcal O(H_\R)$, the abelian subalgebra $\LL(\Z)$ is maximal amenable in the crossed product ${\rm II}_1$ factor $Γ(H_\R)\dpr \rtimes_π\Z$ associated with the free Bogoljubov action of the representation $π$. This provides uncountably many non-isomorphic $A$-$A$-bimodules which are disjoint from the coarse $A$-$A$-bimodule and of the form $\LL^2(M \ominus A)$ where $A \subset M$ is a maximal amenable masa in a ${\rm II_1}$ factor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1203_6743 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | A class of ${\rm II_1}$ factors with an exotic abelian maximal amenable subalgebra Houdayer, Cyril Operator Algebras 46L10, 46L54, 46L55, 22D25 We show that for every mixing orthogonal representation $π: \Z \to \mathcal O(H_\R)$, the abelian subalgebra $\LL(\Z)$ is maximal amenable in the crossed product ${\rm II}_1$ factor $Γ(H_\R)\dpr \rtimes_π\Z$ associated with the free Bogoljubov action of the representation $π$. This provides uncountably many non-isomorphic $A$-$A$-bimodules which are disjoint from the coarse $A$-$A$-bimodule and of the form $\LL^2(M \ominus A)$ where $A \subset M$ is a maximal amenable masa in a ${\rm II_1}$ factor. |
| title | A class of ${\rm II_1}$ factors with an exotic abelian maximal amenable subalgebra |
| topic | Operator Algebras 46L10, 46L54, 46L55, 22D25 |
| url | https://arxiv.org/abs/1203.6743 |