Strong classification of purely infinite Cuntz-Krieger algebras

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.

The current paper uses results and especially the notation developed in arXiv:1604.05439 and arXiv:1602.03709 (that supersede the paper arXiv:1505.06773)

References in corpus (3)

• The complete classification of unital graph $C^{\ast }$-algebras: Geometric and strong
• Geometric classification of graph $C^{\ast }$-algebras over finite graphs
• Strong classification of extensions of classifiable C*-algebras

Cited by in corpus (3)

• The complete classification of unital graph $C^{\ast }$-algebras: Geometric and strong
• The nuclear dimension of ${\mathcal{O}}_{\infty }$-stable $C^{\ast }$-algebras
• Invariance of the Cuntz splice