On the homotopy groups of the automorphism groups of Cuntz–Krieger algebras

In this paper, we first present the homotopy groups of the automorphism groups of Cuntz–Krieger algebras in terms of the underlying matrices defining the Cuntz–Krieger algebras. We also show that the homotopy groups are complete invariants of the isomorphism classes of Cuntz–Krieger algebras. As a result, the isomorphism class of a Cuntz–Krieger algebra is completely determined by the group structure of its weak extension group and strong extension group.