Quasidiagonality of nuclear C*-algebras

Author: 

Tikuisis, A
White, S
Winter, W

Publication Date: 

2017

Journal: 

Annals of Mathematics. Second Series

Last Updated: 

2020-04-03T13:42:58.697+01:00

Issue: 

1

Volume: 

185

DOI: 

10.4007/annals.2017.185.1.4

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

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article