Journal of Operator Theory

Volume 48, Issue 3, Supplementary 2002 pp. 645-662.

Graph inverse semigroups, groupoids and their $C^*$-algebras

Authors: Alan L.T. Paterson
Author institution: Department of Mathematics, University of Mississippi, University, MS 38677, USA

Summary: 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.

Keywords: Directed graphs, graph inverse semigroups, graph groupoids, graph $C^*$-algebras, Cuntz-Krieger algebras, amenability

Contents Full-Text PDF