Mathematics – Operator Algebras
Scientific paper
2007-06-25
Mathematics
Operator Algebras
27 pages; minor modifications; 10/27/07: New version with improved statements, new applications, and simplifications in proofs
Scientific paper
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 $(X,\mu)$ is profinite then the group measure space factor $L^\infty(X)\rtimes \Bbb F_r$ has unique Cartan subalgebra, up to unitary conjugacy.
Ozawa Narutaka
Popa Sorin
No associations
LandOfFree
On a class of $\mathrm{II}_1$ factors with at most one Cartan subalgebra does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On a class of $\mathrm{II}_1$ factors with at most one Cartan subalgebra, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On a class of $\mathrm{II}_1$ factors with at most one Cartan subalgebra will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-230215