Graph inverse semigroups, groupoids and their C*-algebras

Abstract

We develop a theory of graph C*-algebras using path groupoids and inverse semigroups. Row finiteness is not assumed so that the theory applies to graphs for which there are vertices emitting a countably infinite set of edges. We show that the path groupoid is amenable, and give a groupoid proof of a recent theorem of Szymanski characterizing when a graph C*-algebra is simple.

17 pages

Cited by in corpus (2)

• Some intrinsic properties of simple graph $C^{\ast }$-algebras
• A class of C^*-algebras generalizing both graph algebras and homeomorphism C^*-algebras III, ideal structures