Bosa, J., Brown, N. P., Sato, Y., Tikuisis, A., White, S. and Winter, W. (2019) Covering dimension of C*-algebras and 2-coloured classification. Memoirs of the American Mathematical Society, 257(1233), (doi: 10.1090/memo/1233)
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Abstract
We introduce the concept of finitely coloured equivalence for unital *-homomorphisms between C*-algebras, for which unitary equivalence is the 1-coloured case. We use this notion to classify *- homomorphisms from separable, unital, nuclear C*-algebras into ultrapowers of simple, unital, nuclear, Z-stable C*-algebras with compact extremal trace space up to 2-coloured equivalence by their behaviour on traces; this is based on a 1-coloured classification theorem for certain order zero maps, also in terms of tracial data. As an application we calculate the nuclear dimension of non-AF, simple, separable, unital, nuclear, Z-stable C*-algebras with compact extremal trace space: it is 1. In the case that the extremal trace space also has finite topological covering dimension, this confirms the remaining open implication of the Toms-Winter conjecture. Inspired by homotopy-rigidity theorems in geometry and topology, we derive a \homotopy equivalence implies isomorphism" result for large classes of C*-algebras with finite nuclear dimension.
Item Type: | Articles |
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Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | White, Professor Stuart and Bosa, Dr Joan |
Authors: | Bosa, J., Brown, N. P., Sato, Y., Tikuisis, A., White, S., and Winter, W. |
College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
Journal Name: | Memoirs of the American Mathematical Society |
Publisher: | American Mathematical Society |
ISSN: | 0065-9266 |
ISSN (Online): | 1947-6221 |
ISBN: | 9781470434700 |
Published Online: | 10 January 2019 |
Copyright Holders: | Copyright © 2019 American Mathematical Society |
First Published: | First published in Memoirs of the American Mathematical Society 257:1233 |
Publisher Policy: | Reproduced in accordance with the copyright policy of the publisher |
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