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

TL;DR

This paper investigates the structure and stable rank of C*-algebras derived from finite higher-rank graphs, providing complete classifications under certain conditions and illustrating these with examples.

Contribution

It offers a comprehensive analysis of stable rank and unital stably finite conditions for C*-algebras of finite higher-rank graphs, extending existing theory.

Findings

Stable rank determined when the k-graph has no cycle with an entrance or is cofinal.

Exact characterization of when these C*-algebras are unital and stably finite.

Several illustrative examples demonstrating the theoretical results.

Abstract

We 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.