Groupoids and C*-algebras for categories of paths

Details Groupoids and C*-algebras for categories of paths Groupoids and C*-algebras for categories of paths

2011-11-29

arxiv.org/abs/1111.6924v2

Mathematics

Operator Algebras

Section 8: fixed a gap in the construction of the directed boundary of an ordered group, including a larger discussion of the

Scientific paper

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.

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