On a class of II1 factors with at most one Cartan subalgebra

• 成果类型: Article
• 署名作者: Ozawa, Narutaka; Popa, Sorin
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2010.172.713
• 发表日期: 2010
• 页码: 713-749
• 关键词: ergodic equivalence relations; amalgamated free-products; entropy; multipliers; COHOMOLOGY; ALGEBRAS; RIGIDITY; index

摘要

We prove that the normalizer of any diffuse amenable subalgebra of a free group factor L(F-r) generates an amenable von Neumann subalgebra. Moreover, any II1 factor of the form Q (circle times) over barL(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 F-r, 2 <= r <= infinity, on a probability space (X, mu) is profinite then the group measure space factor L-infinity (X) F-r has unique Cartan subalgebra, up to unitary conjugacy.