Annals of Functional Analysis

On certain properties of Cuntz–Krieger-type algebras

Bernhard Burgstaller and D. Gwion Evans

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This note presents a further study of the class of Cuntz–Krieger-type algebras. A necessary and sufficient condition is identified that ensures that the algebra is purely infinite, the ideal structure is studied, and nuclearity is proved by presenting the algebra as a crossed product of an AF-algebra by an abelian group. The results are applied to examples of Cuntz–Krieger-type algebras, such as higher-rank semigraph C-algebras and higher-rank Exel–Laca algebras.

Article information

Ann. Funct. Anal., Volume 8, Number 3 (2017), 386-397.

Received: 29 April 2016
Accepted: 6 November 2016
First available in Project Euclid: 9 May 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46L05: General theory of $C^*$-algebras
Secondary: 46L55: Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]

Cuntz–Krieger semigraph algebra ideal purely infinite crossed product


Burgstaller, Bernhard; Evans, D. Gwion. On certain properties of Cuntz–Krieger-type algebras. Ann. Funct. Anal. 8 (2017), no. 3, 386--397. doi:10.1215/20088752-2017-0004.

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