Strong classification of purely infinite Cuntz-Krieger algebras

TL;DR

This paper advances the classification of purely infinite Cuntz-Krieger algebras by establishing strong and unital classification results, showing that isomorphisms in filtered K-theory lift to *-isomorphisms.

Contribution

It proves that isomorphisms of reduced filtered K-theory lift to *-isomorphisms, achieving strong and unital classification of these algebras.

Findings

Isomorphisms of filtered K-theory lift to *-isomorphisms.

Achieved strong classification of purely infinite Cuntz-Krieger algebras.

Established unital classification results.

Abstract

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-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.