Diagonality of actions and KMS weights

TL;DR

This paper explores the relationship between diagonal actions and KMS weights on groupoid C*-algebras, and applies these concepts to graph C*-algebras via groupoid realizations of local homeomorphisms.

Contribution

It establishes a connection between diagonal actions and KMS weights, and demonstrates how graph C*-algebras can be realized as groupoid C*-algebras of local homeomorphisms.

Findings

Connection between diagonal actions and KMS weights on groupoid C*-algebras.

Realization of graph C*-algebras as groupoid C*-algebras of local homeomorphisms.

Application of the theory to specific classes of graph C*-algebras.

Abstract

The paper contains a description of a connection between diagonal actions and certain KMS weights on groupoid $C^{*}$-algebras. It furthermore contains the realization of a graph $C^{*}$-algebra of a countable graph as the groupoid $C^{*}$-algebra of a local homeomorphism and applies the theory obtained on these algebras.