Geodesic
$C^*$-algebras associated to coverings of $k$-graphs
Documenta mathematica, Tome 13 (2008), pp. 161-205
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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 Pn​ whose K-theory is opposite to that of On​, and a class of AT-algebras that can naturally be regarded as higher-rank Bunce–Deddens algebras.
DOI : 10.4171/dm/247
Classification : 46L05
Mots-clés : C∗-algebra, K-theory, graph algebra, k-graph, covering 
@article{10_4171_dm_247,
     author = {Alex Kumjian and David Pask and Aidan Sims},
     title = {$C^*$-algebras associated to coverings of $k$-graphs},
     journal = {Documenta mathematica},
     pages = {161--205},
     year = {2008},
     volume = {13},
     doi = {10.4171/dm/247},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/247/}
}
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Alex Kumjian; David Pask; Aidan Sims. $C^*$-algebras associated to coverings of $k$-graphs. Documenta mathematica, Tome 13 (2008), pp. 161-205. doi: 10.4171/dm/247

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