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}
}
  • J. Spielberg
  • Published 29 November 2011
  • Mathematics
  • Transactions of the American Mathematical Society
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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