On a Class of Ii1 Factors with at Most One Cartan Subalgebra
نویسندگان
چکیده
We prove that the normalizer of any diffuse amenable subalgebra of a free group factor L(Fr) generates an amenable von Neumann subalgebra. Moreover, any II1 factor of the form Q ⊗̄L(Fr), 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 Fr, 2 ≤ r ≤ ∞, on a probability space (X,μ) is profinite then the group measure space factor L∞(X)⋊Fr has unique Cartan subalgebra, up to unitary conjugacy.
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