English

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 II1\rm II_1 factors of universal orthogonal and unitary discrete quantum groups have no Cartan subalgebras. We also prove that continuous cores of type III1\rm III_1 factors with such a condition are semisolid as a II\rm II_\infty 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