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.