# Groupoids and C * -algebras for categories of paths

@article{Spielberg2011GroupoidsAC, title={Groupoids and C * -algebras for categories of paths}, author={Jack Spielberg}, journal={Transactions of the American Mathematical Society}, year={2011}, volume={366}, pages={5771-5819} }

In this paper we describe a new method of defining C*-algebras from oriented combinatorial data, thereby generalizing the constructions of algebras from directed graphs, higher-rank graphs, and ordered groups. We show that only the most elementary notions of concatenation and cancellation of paths are required to define versions of Cuntz-Krieger and Toeplitz-Cuntz-Krieger algebras, and the presentation by generators and relations follows naturally. We give sufficient conditions for the…

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