Extensions of Cuntz-Krieger algebras

TL;DR

This paper proves that certain C*-algebras resembling Cuntz-Krieger algebras are actually isomorphic to them, demonstrating the class's closure under extensions of real rank zero.

Contribution

It establishes that C*-algebras similar to Cuntz-Krieger algebras are indeed Cuntz-Krieger algebras, showing closure under specific extensions.

Findings

C*-algebras resembling Cuntz-Krieger algebras are isomorphic to them

The class of Cuntz-Krieger algebras is closed under extensions of real rank zero

Provides structural characterization of these algebras

Abstract

We show that a C*-algebra "looking like" a Cuntz-Krieger algebra is a Cuntz-Krieger algebra. This implies that, in an appropriate sense, the class of Cuntz-Krieger algebras is closed under extensions of real rank zero.