Cuntz-Krieger type uniqueness theorem for topological higher-rank graph C*-algebras

Abstract

We study Sims-Yeend's product system C*-algebras and topological higher-rank graph C*-algebras by Yeend. We give a relation between Katsura's Cuntz-Pimsner covariance and Sims-Yeend's one by a direct approach and an explicit form of the core of product system C*-algebras. Finally, we prove Cuntz-Krieger type uniqueness theorem for topological higher-rank graph C*-algebras under certain aperiodic condition.

22 pages; V2 comment: Some typos are corrected. Some sentences are changed.; V3 comment: Title changed, Errors in V2 are fixed

References in corpus (5)

• Higher rank graph C*-algebras
• Product systems of graphs and the Toeplitz algebras of higher-rank graphs
• C*-algebras associated to product systems of Hilbert bimodules
• Topological higher-rank graphs and the $C^{\ast }$-algebras of topological 1-graphs
• Cuntz's $ax+b$-semigroup C*-algebra over $\mathbb{N}$ and product system C*-algebras

Cited by in corpus (3)

• Uniqueness theorems for topological higher-rank graph C*-algebras
• Homology for higher-rank graphs and twisted C*-algebras
• Two families of Exel-Larsen crossed products