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Rank-two graphs whose C^*-algebras are direct limits of circle algebras

David Pask·Iain Raeburn·Mikael Rordam·Aidan Sims
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Abstract

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.

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David Pask, Iain Raeburn, Mikael Rordam, Aidan Sims. 2005-12-13. Rank-two graphs whose C^*-algebras are direct limits of circle algebras. https://arxiv.org/abs/math/0512254

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