On a class of $\mathrm{II}_1$ factors with at most one Cartan subalgebra

dc.creatorOzawa, Narutaka
dc.creatorPopa, Sorin
dc.date2007-06-25
dc.date2007-10-28
dc.date.accessioned2026-07-07T08:38:44Z
dc.date.available2026-07-07T08:38:44Z
dc.descriptionWe prove that the normalizer of any diffuse amenable subalgebra of a free group factor $L(\Bbb F_r)$ generates an amenable von Neumann subalgebra. Moreover, any II$_1$ factor of the form $Q \vt L(\Bbb F_r) $, with $Q$ an arbitrary subfactor of a tensor product of free group factors, has no Cartan subalgebras. We also prove that if a free ergodic measure preserving action of a free group $\Bbb F_r$, $2\leq r \leq \infty$, on a probability space $(X,μ)$ is profinite then the group measure space factor $L^\infty(X)\rtimes \Bbb F_r$ has unique Cartan subalgebra, up to unitary conjugacy.
dc.description27 pages; minor modifications; 10/27/07: New version with improved statements, new applications, and simplifications in proofs
dc.identifierhttps://arxiv.org/abs/0706.3623
dc.identifierhttp://arxiv.org/abs/0706.3623
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/140836
dc.subjectOperator Algebras
dc.subjectGroup Theory
dc.subject46L10 (Primary); 37A20 (Secondary)
dc.titleOn a class of $\mathrm{II}_1$ factors with at most one Cartan subalgebra
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