Examples of factors which have no Cartan subalgebras

Isono, Yusuke

doi:10.1090/tran/6321

Examples of factors which have no Cartan subalgebras
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Trans. Amer. Math. Soc. 367 (2015), 7917-7937 Request permission

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

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