Journal article
Uniform property Gamma
- Abstract:
- We further examine the concept of uniform property Gamma for C*-algebras introduced in our joint work with Winter. In addition to obtaining characterisations in the spirit of Dixmier's work on central sequence in II$_1$ factors, we establish the equivalence of uniform property Gamma, a suitable uniform version of McDuff's property for C*-algebras, and the existence of complemented partitions of unity for separable nuclear C*-algebras with no finite dimensional representations and a compact (non-empty) tracial state space. As a consequence, for C*-algebras as in the Toms-Winter conjecture, the combination of strict comparison and uniform property Gamma is equivalent to Jiang-Su stability. We also show how these ideas can be combined with those of Matui-Sato to streamline Winter's classification-by-embeddings technique.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Accepted manuscript, pdf, 503.8KB, Terms of use)
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- Publisher copy:
- 10.1093/imrn/rnaa282
Authors
- Publisher:
- Oxford University Press
- Journal:
- International Mathematics Research Notices More from this journal
- Volume:
- 2022
- Issue:
- 13
- Pages:
- 9864–9908
- Publication date:
- 2021-02-13
- Acceptance date:
- 2020-09-23
- DOI:
- EISSN:
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1687-0247
- ISSN:
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1073-7928
- Language:
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English
- Keywords:
- Pubs id:
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1077592
- Local pid:
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pubs:1077592
- Deposit date:
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2021-02-25
- ARK identifier:
Terms of use
- Copyright holder:
- Castillejos et al.
- Copyright date:
- 2021
- Rights statement:
- © The Author(s) 2021. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: [email protected].
- Notes:
- This is the accepgted manuscript version of the article. The final version is available online from Oxford University Press at: http://dx.doi.org/10.1093/imrn/rnaa282
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