$C^*$-algebras associated to coverings of $k$-graphs

@article{Kumjian2006CalgebrasAT,
  title={\$C^*\$-algebras associated to coverings of \$k\$-graphs},
  author={Alex Kumjian and David Pask and Aidan Sims},
  journal={Documenta Mathematica},
  year={2006}
}
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… 

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