Examples of factors which have no Cartan subalgebras

Abstract

We consider some conditions similar to Ozawa's condition (AO), and prove that if a non-injective factor satisfies such a condition and has the W*CBAP, then it has no Cartan subalgebras. As a corollary, we prove that $\mathrm{I}{\mathrm{I}}_1$ factors of universal orthogonal and unitary discrete quantum groups have no Cartan subalgebras. We also prove that continuous cores of type $\mathrm{II}{\mathrm{I}}_1$ factors with such a condition are semisolid as a $\mathrm{I}{\mathrm{I}}_{\infty }$ factor.

21 pages, final version, to appear in Trans. Amer. Math. Soc

References in corpus (4)

• On a Class of Type II${}_1$ Factors with Betti Numbers Invariants
• Orientation of quantum Cayley trees and applications
• Some estimates for non-microstates free entropy dimension, with applications to $q$-semicircular families
• Weak Exactness for C*-algebras and Application to Condition (AO)

Cited by in corpus (3)

• CCAP for universal discrete quantum groups
• The Connes embedding property for quantum group von Neumann algebras
• Strong asymptotic freeness for free orthogonal quantum groups