Examples of factors which have no Cartan subalgebras

Yusuke Isono

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arXiv · 1209.1728

Examples of factors which have no Cartan subalgebras

Yusuke Isono

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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 $\rm II_1$ 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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Yusuke Isono. 2014-01-27. Examples of factors which have no Cartan subalgebras. https://arxiv.org/abs/1209.1728

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