%0 Journal Article
%T C*-algebras associated to coverings of k-graphs
%A Alex Kumjian
%A David Pask
%A Aidan Sims
%J Mathematics
%D 2006
%I arXiv
%X A covering of k-graphs (in the sense of Pask-Quigg-Raeburn) induces an embedding of universal C*-algebras. We show how to build a (k+1)-graph whose universal algebra encodes this embedding. More generally we show how to realise a direct limit of k-graph algebras under embeddings induced from coverings as the universal algebra of a (k+1)-graph. Our main focus is on computing the K-theory of the (k+1)-graph algebra from that of the component k-graph algebras. Examples of our construction include a realisation of the Kirchberg algebra \mathcal{P}_n whose K-theory is opposite to that of \mathcal{O}_n, and a class of AT-algebras that can naturally be regarded as higher-rank Bunce-Deddens algebras.
%U http://arxiv.org/abs/math/0612204v3