English

Higher-rank graphs and their C*-algebras

Operator Algebras 2007-05-23 v1 Combinatorics

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.

Keywords

Cite

@article{arxiv.math/0107222,
  title  = {Higher-rank graphs and their C*-algebras},
  author = {Iain Raeburn and Aidan Sims and Trent Yeend},
  journal= {arXiv preprint arXiv:math/0107222},
  year   = {2007}
}
R2 v1 2026-07-22T16:39:48.558Z