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| Format: | Preprint |
| Publicat: |
2012
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| Matèries: | |
| Accés en línia: | https://arxiv.org/abs/1209.5209 |
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| _version_ | 1866912485066407936 |
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| author | Houdayer, Cyril |
| author_facet | Houdayer, Cyril |
| contents | In this paper, we investigate several structural properties for crossed product ${\rm II_1}$ factors $M$ arising from free Bogoljubov actions associated with orthogonal representations $π: G \to \mathcal O(H_\mathbf R)$ of arbitrary countable discrete groups. Under fairly general assumptions on the orthogonal representation $π: G \to \mathcal O(H_{\mathbf R})$, we show that $M$ does not have property Gamma of Murray and von Neumann. Then we show that any regular amenable subalgebra $A \subset M$ can be embedded into $L(G)$ inside $M$. Finally, when $G$ is assumed to be amenable, we locate precisely any possible amenable or Gamma extension of $L(G)$ inside $M$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1209_5209 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | Structure of ${\rm II_1}$ factors arising from free Bogoljubov actions of arbitrary groups Houdayer, Cyril Operator Algebras Functional Analysis 46L10, 46L54, 46L55, 22D25 In this paper, we investigate several structural properties for crossed product ${\rm II_1}$ factors $M$ arising from free Bogoljubov actions associated with orthogonal representations $π: G \to \mathcal O(H_\mathbf R)$ of arbitrary countable discrete groups. Under fairly general assumptions on the orthogonal representation $π: G \to \mathcal O(H_{\mathbf R})$, we show that $M$ does not have property Gamma of Murray and von Neumann. Then we show that any regular amenable subalgebra $A \subset M$ can be embedded into $L(G)$ inside $M$. Finally, when $G$ is assumed to be amenable, we locate precisely any possible amenable or Gamma extension of $L(G)$ inside $M$. |
| title | Structure of ${\rm II_1}$ factors arising from free Bogoljubov actions of arbitrary groups |
| topic | Operator Algebras Functional Analysis 46L10, 46L54, 46L55, 22D25 |
| url | https://arxiv.org/abs/1209.5209 |