Corners of Cuntz-Krieger algebras

Abstract

We show that if $A$ is a unital $C^{\ast }$-algebra and $B$ is a Cuntz-Krieger algebra for which $A\otimes \mathbb{K}\cong B\otimes \mathbb{K}$, then $A$ is a Cuntz-Krieger algebra. Consequently, corners of Cuntz-Krieger algebras are Cuntz-Krieger algebras.

Version 3: 20 pages. Corrected typos and added or clarified definitions. This is the version that will be published. Version 2: 18 pages, removed unnecessary assumptions in Theorem 3.5 and Corollary 3.6, and updated references

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