A class of Exel--Laca algebras reciprocal to Cuntz--Krieger algebras

Abstract

The reciprocality means a duality in Kirchberg algebras between K-theory groups and strong extension groups. In the paper, we will find a certain class of unital simple Exel--Laca algebras for which the reciprocal duals are simple Cuntz--Krieger algebras in terms of the underlying infinite matrices. In our procedure to obtain simple Cuntz--Krieger algebras from Exel--Laca algebras, we compute the strong extension groups for Exel--Laca algebras belonging to the class.