# Higher Rank Graph C-Algebras

@article{Kumjian2000HigherRG, title={Higher Rank Graph C-Algebras}, author={Alex Kumjian and David Pask}, journal={arXiv: Operator Algebras}, year={2000} }

Building on recent work of Robertson and Steger, we associate a C{algebra to a combinatorial object which may be thought of as a higher rank graph. This C{algebra is shown to be isomorphic to that of the associ- ated path groupoid. Various results in this paper give sucient conditions on the higher rank graph for the associated C{algebra to be: simple, purely in- nite and AF. Results concerning the structure of crossed products by certain natural actions of discrete groups are obtained; a…

## 160 Citations

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