Higher-rank graphs and their C*-algebras

Iain Raeburn*, Aidan Sims, Trent Yeend

*Corresponding author for this work

Research output: Contribution to journalArticle

83 Citations (Scopus)

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 characterizes the higher-rank graphs that admit a non-trivial Cuntz-Krieger family. We then prove versions of the uniqueness theorems and classifications of ideals for the C*-algebras generated by Cuntz-Krieger families.

Original languageEnglish
Pages (from-to)99-115
Number of pages17
JournalProceedings of the Edinburgh Mathematical Society
Volume46
Issue number1
DOIs
Publication statusPublished - Feb 2003
Externally publishedYes

Keywords

  • Cuntz-Krieger algebra
  • graph algebra
  • uniqueness

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