Groupoids and $C^*$-algebras for categories of paths
Groupoids and $C^*$-algebras for categories of paths
In this paper we describe a new method of defining $C^*$-algebras from oriented combinatorial data, thereby generalizing the construction 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 …