On the K-Theory of Cuntz–Krieger Algebras

Abstract

We extend the uniqueness and simplicity results of Cuntz and Krieger to the countably infinite case, under a row-finite condition on the matrix $A$. Then we present a new approach to calculating the K-theory of the Cuntz–Krieger algebras, using the gauge action of $\mathbf{T}$, which also works when $A$ is a countably infinite $0$-$1$ matrix. This calculation uses a dual Pimsner-Voiculescu six-term exact sequence for algebras carrying an action of $\mathbf{T}$. Finally, we use these new results to calculate the K-theory of the Doplicher–Roberts algebras.