Rank-two graphs whose [formula omitted]-algebras are direct limits of circle algebras

Abstract

We describe a class of rank-2 graphs whose C ∗ -algebras are A T 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.