Author
Tikuisis, A
White, S
Winter, W
Journal title
Annals of Mathematics
DOI
10.4007/annals.2017.185.1.4
Issue
1
Volume
185
Last updated
2022-01-12T13:10:09.06+00:00
Page
229-284
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.
Symplectic ID
1049971
Favourite
On
Publication type
Journal Article
Publication date
01 Jan 2017