Higher-rank graphs and their C*-algebras

Iain Raeburn; Aidan Sims; Trent Yeend

doi:10.1017/S0013091501000645

Higher-rank graphs and their C*-algebras

Iain Raeburn^*, Aidan Sims, Trent Yeend

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

99 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 language	English
Pages (from-to)	99-115
Number of pages	17
Journal	Proceedings of the Edinburgh Mathematical Society
Volume	46
Issue number	1
DOIs	https://doi.org/10.1017/S0013091501000645
Publication status	Published - Feb 2003
Externally published	Yes

Keywords

Cuntz-Krieger algebra
graph algebra
uniqueness

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10.1017/S0013091501000645

Cite this

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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.",

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AB - 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.

KW - Cuntz-Krieger algebra

KW - graph algebra

KW - uniqueness

UR - https://www.scopus.com/pages/publications/0037298755

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DO - 10.1017/S0013091501000645

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Higher-rank graphs and their C*-algebras

Abstract

Keywords

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