Quasidiagonality of nuclear C*-algebras

Tikuisis, A., White, S. and Winter, W. (2017) Quasidiagonality of nuclear C*-algebras. Annals of Mathematics, 185(1), pp. 229-284. (doi:10.4007/annals.2017.185.1.4)

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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.

Item Type:Articles
Additional Information:Research partially supported by EPSRC (EP/N002377), NSERC (PDF, held by AT), by an Alexander von Humboldt foundation fellowship (held by SW) and by the DFG (SFB 878).
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:White, Professor Stuart
Authors: Tikuisis, A., White, S., and Winter, W.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Annals of Mathematics
Publisher:Mathematical Sciences Publishers
ISSN:0003-486X
ISSN (Online):1939-8980
Published Online:02 December 2016
Copyright Holders:Copyright © 2017 Department of Mathematics, Princeton University
First Published:First published in Annals of Mathematics 185(1): 229-284
Publisher Policy:Reproduced in accordance with the publisher copyright policy

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