Structure of II₁ factors arising from free Bogoljubov actions of arbitrary groups

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• 作者：Cyril Houdayer ^{cyril.houdayer@ens-lyon.fr" class="auth_mail}
• 关键词：46L10 ; 46L54 ; 46L55 ; 22D25
• 刊名：Advances in Mathematics
• 出版年：1 August 2014
• 年：2014
• 卷：260
• 期：Complete
• 页码：414-457
• 全文大小：599 K

文摘

In this paper, we investigate several structural properties for crossed product II₁ factors M   arising from free Bogoljubov actions associated with orthogonal representations 蟺:G→O(H_R)$蟺:G\to \mathcal{O}(H_{\mathbf{R}})$ of arbitrary countable discrete groups. Under fairly general assumptions on the orthogonal representation 蟺:G→O(H_R)$蟺:G\to \mathcal{O}(H_{\mathbf{R}})$, we show that M   does not have property Gamma of Murray and von Neumann. Then we show that any regular amenable subalgebra A⊂M$A\subset M$ can be embedded into L(G)$\mathrm{L}(G)$ inside M  . Finally, when G   is assumed to be amenable, we locate precisely any possible amenable or Gamma extension of L(G)$\mathrm{L}(G)$ inside M.