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

@article{Raeburn2001HIGHERRANKGA, title={HIGHER-RANK GRAPHS AND THEIR \$C^*\$-ALGEBRAS}, author={Iain Raeburn and Aidan Sims and Trent Yeend}, journal={Proceedings of the Edinburgh Mathematical Society}, year={2001}, volume={46}, pages={99 - 115} }

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. AMS 2000…

## 140 Citations

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