Structure theory and stable rank for C*-algebras of finite higher-rank graphs

Abstract

We study the structure and compute the stable rank of C * -algebras of finite higher-rank graphs. We obtain a complete characterisation when the k-graph C * -algebra is stably finite, and also when the k-graph is cofinal. In the process, we determine exactly which finite k-graphs yield unital stably finite C * -algebras and we give several examples to illustrate our results.