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.

arXiv comment14 pages

References in corpus (2)

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

Cited by in corpus (12)

• Nuclear dimension of simple C*-algebras
• Nuclear dimension and Z-stability
• Tensor products and regularity properties of Cuntz semigroups
• Regularity properties and Rokhlin dimension for compact group actions
• Central sequence C*-algebras and tensorial absorption of the Jiang-Su algebra
• Actions of amenable groups and crossed products of Z-absorbing C*-algebras
• Uniform property Gamma
• Dixmier approximation and symmetric amenability for C*-algebras
• Strict comparison for $C^{\ast }$-algebras arising from Almost finite groupoids
• 2-positive almost order zero maps and decomposition rank
• Tracial state space with non-compact extreme boundary
• Invariant ergodic measures and the classification of crossed product $C^{\ast }$-algebras