A note on crossed products of rotation algebras

Abstract

We compute the K-theory of crossed products of rotation algebras Aθ, for any real angle θ, by matrices in SL(2,Z) with infinite order. Using techniques of continuous fields, we show that the canonical inclusion of Aθ into the crossed products is injective at the level of K0-groups. We then give an explicit set of generators for the K0-groups and compute the tracial ranges concretely.