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

Published online by Cambridge University Press:  27 January 2003

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)
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Abstract

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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.

AMS 2000 Mathematics subject classification: Primary 46L05

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2003