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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121742.pdf - Accepted Version 667kB |
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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