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arXiv · 1912.04207

Uniform property Gamma

Jorge Castillejos·Samuel Evington·Aaron Tikuisis·Stuart White
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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.

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Jorge Castillejos, Samuel Evington, Aaron Tikuisis, Stuart White. 2019-12-09. Uniform property Gamma. https://arxiv.org/abs/1912.04207

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