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.

Contents Full-Text PDF