C*-algebras associated to coverings of k-graphs

Details C*-algebras associated to coverings of k-graphs C*-algebras associated to coverings of k-graphs

2006-12-08

arxiv.org/abs/math/0612204v3

Mathematics

Operator Algebras

44 pages, 2 figures, some diagrams drawn using picTeX. v2. A number of typos corrected, some references updated. The statement

Scientific paper

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.

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