-algebras associated to coverings of -graphs

  • Alex Kumjian

    Department of Mathematics (084) School of Mathematics and University of Nevada Applied Statistics Reno NV 89557-0084 University of Wollongong USA NSW 2522
  • David Pask

  • Aidan Sims

    School of Mathematics and Applied Statistics University of Wollongong NSW 2522 AUSTRALIA
$C^*$-algebras associated to coverings of $k$-graphs cover
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A covering of -graphs (in the sense of Pask–Quigg–Raeburn) induces an embedding of universal -algebras. We show how to build a -graph whose universal algebra encodes this embedding. More generally we show how to realise a direct limit of -graph algebras under embeddings induced from coverings as the universal algebra of a -graph. Our main focus is on computing the -theory of the -graph algebra from that of the component -graph algebras. Examples of our construction include a realisation of the Kirchberg algebra whose -theory is opposite to that of , and a class of A-algebras that can naturally be regarded as higher-rank Bunce–Deddens algebras.

Cite this article

Alex Kumjian, David Pask, Aidan Sims, -algebras associated to coverings of -graphs. Doc. Math. 13 (2008), pp. 161–205

DOI 10.4171/DM/247