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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 ([email protected]; [email protected]; [email protected])
Aidan Sims
Affiliation:
Department of Mathematics, University of Newcastle, Callaghan, NSW 2308, Australia ([email protected]; [email protected]; [email protected])
Trent Yeend
Affiliation:
Department of Mathematics, University of Newcastle, Callaghan, NSW 2308, Australia ([email protected]; [email protected]; [email protected])
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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. 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