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 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 T. Finally, we use these new results to calculate the K-theory of the Doplicher-Roberts algebras.
Cite this article
David Pask, Iain Raeburn, On the K-Theory of Cuntz-Krieger Algebras. Publ. Res. Inst. Math. Sci. 32 (1996), no. 3, pp. 415–443DOI 10.2977/PRIMS/1195162850