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

2012/09/24 by Cyril Houdayer, Houdayer, Cyril
Mathematics · #22D25 #46L10 #46L54 #46L55 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1209.5209

openalex publication_date 2012/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate several structural properties for crossed product \rm II₁ factors M arising from free Bogoljubov actions associated with orthogonal representations π: G → \mathcal O(H_\mathbf R) of arbitrary countable discrete groups. Under fairly general assumptions on the orthogonal representation π: G → \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 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.

Citations

• A class of \rm II₁ factors with an exotic abelian maximal amenable subalgebra

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