Z-Stability and Finite-Dimensional Tracial Boundaries
Z-Stability and Finite-Dimensional Tracial Boundaries
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.