We describe a class of rank-2 graphs whose C*-algebras are AT algebras. For a subclass which we call rank-2 Bratteli diagrams, we compute the K-theory of the C*-algebra.We identify rank-2 Bratteli diagrams whose C*-algebras are simple and have real-rank zero, and characterise the K-invariants achieved by such algebras. We give examples of rank-2 Bratteli diagrams whose C*-algebras contain as full corners the irrational rotation algebras and the Bunce–Deddens algebras.
Journal of Functional Analysis Vol. 239, Issue 1, p. 137-178