Structure theory and stable rank for C*-algebras of finite higher-rank graphs. Issue 4 (4th November 2021)

• Record Type: Journal Article
• Authors: Pask, David; Sierakowski, Adam; Sims, Aidan
• Is Part Of: Proceedings of the Edinburgh Mathematical Society. Volume 64:Issue 4(2021)
• Page Start: 822
• Page End: 847
• Publication Date: 2021-11-04
• Subjects: higher-rank graph -- stable rank -- C*-algebra -- operator algebra; 46L05; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0013091521000626
• Languages: English
• ISSNs: 0013-0915

Abstract

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.