Examples of factors which have no Cartan subalgebras
Operator Algebras
2014-01-28 v3
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 factors of universal orthogonal and unitary discrete quantum groups have no Cartan subalgebras. We also prove that continuous cores of type factors with such a condition are semisolid as a factor.
Keywords
Cite
@article{arxiv.1209.1728,
title = {Examples of factors which have no Cartan subalgebras},
author = {Yusuke Isono},
journal= {arXiv preprint arXiv:1209.1728},
year = {2014}
}
Comments
21 pages, final version, to appear in Trans. Amer. Math. Soc