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

Abstract

AbstractWe study the structure and compute the stable rank of$C^{*}$-algebras of finite higher-rank graphs. We completely determine the stable rank of the$C^{*}$-algebra when the$k$-graph either contains no cycle with an entrance or is cofinal. We also determine exactly which finite, locally convex$k$-graphs yield unital stably finite$C^{*}$-algebras. We give several examples to illustrate our results.