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 (23)

• Graded Steinberg algebras and their representations
• Partial actions and KMS states on relative graph $C^{\ast }$-algebras
• Topological Graph Inverse Semigroups
• Zeta functions and topological entropy of the Markov-Dyck shifts
• A categorical invariant of flow equivalence of shifts
• A Groupoid Approach to Discrete Inverse Semigroup Algebras
• The dynamics of partial inverse semigroup actions
• Two-sided shift spaces over infinite alphabets
• Uniqueness theorems for topological higher-rank graph C*-algebras
• Strong Morita Equivalence of Inverse Semigroups
• Some intrinsic properties of simple graph $C^{\ast }$-algebras
• Algebraic Topology Foundations of Supersymmetry and Symmetry Breaking in Quantum Field Theory and Quantum Gravity: A Review
• The Structure of Line Bundles over Quantum Teardrops
• Branching of Representations to Symmetric Subgroups
• Simplicity of ultragraph algebras
• Ultragraph C*-algebras via topological quivers
• On an order based construction of a groupoid from an inverse semigroup
• Exchange rings and real rank zero C*-algebras associated with finitely separated graphs
• Pure infiniteness and paradoxicality for graph $C^{\ast }$-algebras
• Categorising the operator algebras of groupoids and higher-rank graphs
• Limits of KMS states on Toeplitz algebras of finite graphs
• Closed inverse subsemigroups of graph inverse semigroups
• A class of C^*-algebras generalizing both graph algebras and homeomorphism C^*-algebras III, ideal structures