Quasidiagonality of nuclear C*-algebras
Operator Algebras
2016-12-07 v2
Abstract
We prove that faithful traces on separable and nuclear C*-algebras in the UCT class are quasidiagonal. This has a number of consequences. Firstly, by results of many hands, the classification of unital, separable, simple and nuclear C*-algebras of finite nuclear dimension which satisfy the UCT is now complete. Secondly, our result links the finite to the general version of the Toms-Winter conjecture in the expected way and hence clarifies the relation between decomposition rank and nuclear dimension. Finally, we confirm the Rosenberg conjecture: discrete, amenable groups have quasidiagonal C*-algebras.
Cite
@article{arxiv.1509.08318,
title = {Quasidiagonality of nuclear C*-algebras},
author = {Aaron Tikuisis and Stuart White and Wilhelm Winter},
journal= {arXiv preprint arXiv:1509.08318},
year = {2016}
}
Comments
48 pages; minor changes. Ann. of Math., to appear