Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 8, Number 3 (2017), 386-397.
On certain properties of Cuntz–Krieger-type algebras
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 -algebras and higher-rank Exel–Laca algebras.
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
Permanent link to this document
Digital Object Identifier
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]
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. https://projecteuclid.org/euclid.afa/1494295270