Trace spaces of simple nuclear C*-algebras with finite-dimensional extreme boundary

Abstract

Let A be a unital separable simple infinite-dimensional nuclear C*-algebra with at least one tracial state. We prove that if the trace space of A has compact finite-dimensional extreme boundary then there exist unital embeddings of matrix algebras into a certain central sequence algebra of A which is determined by the uniform topology on the trace space. As an application, it is shown that if furthermore A has strict comparison then A absorbs the Jiang-Su algebra tensorially.

14 pages

References in corpus (2)

• Completely positive maps of order zero
• Strongly self-absorbing C*-algebras are Z-stable

Cited by in corpus (2)

• Actions of amenable groups and crossed products of Z-absorbing C*-algebras
• Strict comparison for $C^{\ast }$-algebras arising from Almost finite groupoids