Higher-rank graphs and their C*-algebras

Authors

Iain Raeburn, University of NewcastleFollow
Aidan Sims, University of WollongongFollow
Trent Yeend, University of NewcastleFollow

RIS ID

16533

Publication Details

Raeburn, I., Sims, A. & Yeend, T. (2003). Higher-rank graphs and their C*-algebras. Proceedings of the Edinburgh Mathematical Society, 46 (1), 99-115.

Abstract

We consider the higher-rank graphs introduced by Kumjian and Pask as models for higher-rank Cuntz-Krieger algebras. We describe a variant of the Cuntz-Krieger relations which applies to graphs with sources, and describe a local convexity condition which characterises the higher-rank graphs that admit a nontrivial Cuntz-Krieger family. We then prove versions of the uniqueness theorems and classifications of ideals for the C*-algebras generated by Cuntz-Krieger families.