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

Abstract

We show that a simple separable unital nuclear nonelementary $C^{\ast }$-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 $\mathbb{Z}$-stability for these algebras.

20 Pages, minor typos fixed

Cited by in corpus (4)

• Quasidiagonality of nuclear C*-algebras
• Nuclear dimension and Z-stability of non-simple C*-algebras
• Equivariant property (SI) revisited
• Variations of projectivity for C*-algebras