Groupoids and C*-algebras for categories of paths

Abstract

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 existence of an AF core, hence of the nuclearity of the C*-algebras, and for aperiodicity, which is used to prove the standard uniqueness theorems.

Prepublication Draft: to appear in the Transactions of the AMS. Many small changes, including motivation for the definition of a zigzag. V. 4 includes the fixing of a gap in the statement and proof of Theorem 6.1

References in corpus (4)

• C*-algebras for categories of paths asociated to the Baumslag-Solitar groups
• $C^{\ast }$-algebra of the $\mathds{Z}^n$-tree
• Graph-Based Models for Kirchberg Algebras
• Co-universal C*-algebras associated to generalised graphs

Cited by in corpus (1)

• C*-algebras for categories of paths asociated to the Baumslag-Solitar groups