On certain properties of Cuntz-Krieger-type algebras

The 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.