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 ∗ C B A P \rm W^*CBAP , then it has no Cartan subalgebras. As a corollary, we prove that I I 1 \rm II_1 factors of universal orthogonal and unitary discrete quantum groups have no Cartan subalgebras. We also prove that continuous cores of type I I I 1 \rm III_1 factors with such a condition are semisolid as a I I ∞ \rm II_\infty factor.