On certain properties of Cuntz--Krieger type algebras

Details On certain properties of Cuntz--Krieger type algebras On certain properties of Cuntz--Krieger type algebras

2011-11-18

arxiv.org/abs/1111.4399v1

Mathematics

Operator Algebras

Scientific paper

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 applied to semigraph algebras, 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.

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