The C*-algebras of finitely aligned higher-rank graphs

Iain Raeburn; Aidan Sims; Trent Yeend

doi:10.1016/j.jfa.2003.10.014

The C*-algebras of finitely aligned higher-rank graphs

Iain Raeburn^*, Aidan Sims, Trent Yeend

^*Corresponding author for this work

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

91 Citations (Scopus)

Abstract

We generalise the theory of Cuntz-Krieger families and graph algebras to the class of finitely aligned k-graphs. This class contains in particular all row-finite k-graphs. The Cuntz-Krieger relations for non-row-finite k-graphs look significantly different from the usual ones, and this substantially complicates the analysis of the graph algebra. We prove a gauge-invariant uniqueness theorem and a Cuntz-Krieger uniqueness theorem for the C*-algebras of finitely aligned k-graphs.

Original language	English
Pages (from-to)	206-240
Number of pages	35
Journal	Journal of Functional Analysis
Volume	213
Issue number	1
DOIs	https://doi.org/10.1016/j.jfa.2003.10.014
Publication status	Published - 1 Aug 2004
Externally published	Yes

Keywords

Cuntz-Krieger algebra
graph algebra
uniqueness

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10.1016/j.jfa.2003.10.014

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abstract = "We generalise the theory of Cuntz-Krieger families and graph algebras to the class of finitely aligned k-graphs. This class contains in particular all row-finite k-graphs. The Cuntz-Krieger relations for non-row-finite k-graphs look significantly different from the usual ones, and this substantially complicates the analysis of the graph algebra. We prove a gauge-invariant uniqueness theorem and a Cuntz-Krieger uniqueness theorem for the C*-algebras of finitely aligned k-graphs.",

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AU - Sims, Aidan

AU - Yeend, Trent

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N2 - We generalise the theory of Cuntz-Krieger families and graph algebras to the class of finitely aligned k-graphs. This class contains in particular all row-finite k-graphs. The Cuntz-Krieger relations for non-row-finite k-graphs look significantly different from the usual ones, and this substantially complicates the analysis of the graph algebra. We prove a gauge-invariant uniqueness theorem and a Cuntz-Krieger uniqueness theorem for the C*-algebras of finitely aligned k-graphs.

AB - We generalise the theory of Cuntz-Krieger families and graph algebras to the class of finitely aligned k-graphs. This class contains in particular all row-finite k-graphs. The Cuntz-Krieger relations for non-row-finite k-graphs look significantly different from the usual ones, and this substantially complicates the analysis of the graph algebra. We prove a gauge-invariant uniqueness theorem and a Cuntz-Krieger uniqueness theorem for the C*-algebras of finitely aligned k-graphs.

KW - Cuntz-Krieger algebra

KW - graph algebra

KW - uniqueness

UR - https://www.scopus.com/pages/publications/3042816922

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DO - 10.1016/j.jfa.2003.10.014

M3 - Article

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VL - 213

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EP - 240

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

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ER -

The C*-algebras of finitely aligned higher-rank graphs

Abstract

Keywords

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