# $C^*$-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…

## 18 Citations

### Twisted k-Graph Algebras Associated to Bratteli Diagrams

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Given a system of coverings of k-graphs, we show that the second cohomology of the resulting (k + 1)-graph is isomorphic to that of any one of the k-graphs in the system, and compute the semifinite…

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Abstract We study the structure and compute the stable rank of $C^{*}$-algebras of finite higher-rank graphs. We completely determine the stable rank of the $C^{*}$-algebra when the $k$-graph either…

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