Strong classification of purely infinite Cuntz-Krieger algebras

In 2006, Restorff completed the classification of all Cuntz-Krieger algebras with finitely many ideals ( i.e. , those that are purely infinite) up to stable isomorphism. He left open the questions concerning strong classification up to stable isomorphism and unital classification. In this paper, we address both questions. We show that any isomorphism between the reduced filtered K K -theory of two Cuntz-Krieger algebras with finitely many ideals lifts to a ∗ ^* -isomorphism between the stabilized Cuntz-Krieger algebras. As a result, we also obtain strong unital classification.