On a class of $\mathrm{II}_1$ factors with at most one Cartan subalgebra
| dc.creator | Ozawa, Narutaka | |
| dc.creator | Popa, Sorin | |
| dc.date | 2007-06-25 | |
| dc.date | 2007-10-28 | |
| dc.date.accessioned | 2026-07-07T08:38:44Z | |
| dc.date.available | 2026-07-07T08:38:44Z | |
| dc.description | We 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.description | 27 pages; minor modifications; 10/27/07: New version with improved statements, new applications, and simplifications in proofs | |
| dc.identifier | https://arxiv.org/abs/0706.3623 | |
| dc.identifier | http://arxiv.org/abs/0706.3623 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/140836 | |
| dc.subject | Operator Algebras | |
| dc.subject | Group Theory | |
| dc.subject | 46L10 (Primary); 37A20 (Secondary) | |
| dc.title | On a class of $\mathrm{II}_1$ factors with at most one Cartan subalgebra | |
| dc.type | text |