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 |
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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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