Graph inverse semigroups, groupoids and their C*-algebras

2003/04/23 by Alan L. T. Paterson · 3 citations
Mathematics · #math.OA #msc:20M18 #msc:22A22 #msc:46L05

paper · pdf

published as J. Operator Theory 48(2002), 645-662 · 17 pages

arxiv created 2003/04/23 · arxiv updated 2009/11/30

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.

Cited by

• Simplicity of algebras and C^*-algebras of self-similar groupoids
• On the structure and skeletals of principal ideal graphs of inverse semigroups
• Groupoid models for relative Cuntz-Pimsner algebras of groupoid correspondences

Related

• Graph inverse semigroups: their characterization and completion
• Graph inverse semigroups and Leavitt path algebras
• Graph inverse semigroups and their substructures
• An inverse semigroup approach to self-similar k-graph C^*-algebras and simplicity
• Groupoids viewed as inverse semigroups