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arXiv · 1209.3292

$\mathcal Z$-stability and finite dimensional tracial boundaries

Andrew Toms·Stuart White·Wilhelm Winter
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Abstract

We show that a simple separable unital nuclear nonelementary $C^*$-algebra whose tracial state space has a compact extreme boundary with finite covering dimension admits uniformly tracially large order zero maps from matrix algebras into its central sequence algebra. As a consequence, strict comparison implies $\Z$-stability for these algebras.

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Andrew Toms, Stuart White, Wilhelm Winter. 2012-09-21. $\mathcal Z$-stability and finite dimensional tracial boundaries. https://doi.org/10.1093/imrn%2Frnu001

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