Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-26T05:45:07.138Z Has data issue: false hasContentIssue false
  • English
  • Français

HIGHER-RANK GRAPHS AND THEIR $C^*$-ALGEBRAS

Published online by Cambridge University Press:  27 January 2003

Iain Raeburn ,
Aidan Sims  and
Trent Yeend
Iain Raeburn
Affiliation:
Department of Mathematics, University of Newcastle, Callaghan, NSW 2308, Australia (iain@maths.newcastle.edu.au; aidan@maths.newcastle.edu.au; trent@maths.newcastle.edu.au)
Aidan Sims
Affiliation:
Department of Mathematics, University of Newcastle, Callaghan, NSW 2308, Australia (iain@maths.newcastle.edu.au; aidan@maths.newcastle.edu.au; trent@maths.newcastle.edu.au)
Trent Yeend
Affiliation:
Department of Mathematics, University of Newcastle, Callaghan, NSW 2308, Australia (iain@maths.newcastle.edu.au; aidan@maths.newcastle.edu.au; trent@maths.newcastle.edu.au)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We consider the higher-rank graphs introduced by Kumjian and Pask as models for higher-rank Cuntz–Krieger algebras. Wedescribe a variant of the Cuntz–Krieger relations which applies to graphs with sources, and describe a local convexitycondition which characterizes the higher-rank graphs that admit a non-trivial Cuntz–Krieger family. We then proveversions of the uniqueness theorems and classifications of ideals for the $C^*$-algebras generated by Cuntz–Krieger families.

AMS 2000 Mathematics subject classification: Primary 46L05

Keywords

graph algebraCuntz–Krieger algebrauniqueness
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 46 , Issue 1 , February 2003 , pp. 99 - 115
Copyright
Copyright © Edinburgh Mathematical Society 2003