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- Title
Uniform Property Γ.
- Authors
Castillejos, Jorge; Evington, Samuel; Tikuisis, Aaron; White, Stuart
- Abstract
We further examine the concept of uniform property |$\Gamma $| for |$C^*$| -algebras introduced in our joint work with Winter. In addition to obtaining characterisations in the spirit of Dixmier's work on central sequences in II |$_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.
- Subjects
UNIFORM algebras; WINTER; LOGICAL prediction; FINITE, The
- Publication
IMRN: International Mathematics Research Notices, 2022, Vol 2022, Issue 13, p9864
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnaa282