# Quasidiagonality of nuclear C*-algebras

Tikuisis, A
White, S
Winter, W

2017

## Journal:

Annals of Mathematics. Second Series

## Last Updated:

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

1

185

## DOI:

10.4007/annals.2017.185.1.4

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.

1049971

Submitted

Journal Article