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

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.