The structure of KMS weights on \'etale groupoid $C^{*}$-algebras

TL;DR

This paper extends classical results on KMS states to KMS weights within the framework of étale groupoid $C^*$-algebras, broadening the understanding of equilibrium states in operator algebras.

Contribution

It generalizes Neshveyev's Theorem to KMS weights for $C^*$-dynamical systems associated with étale groupoids, expanding the theoretical framework.

Findings

Generalization of classical results to KMS weights

Extension of Neshveyev's Theorem to this setting

Broader understanding of KMS states in groupoid $C^*$-algebras

Abstract

We generalise a number of classical results from the theory of KMS states to KMS weights in the setting of $C^{*}$-dynamical systems arising from a continuous groupoid homomorphism $c:\mathcal{G} \to \mathbb{R}$ on a locally compact second countable Hausdorff \'etale groupoid $\mathcal{G}$. In particular, we generalise Neshveyev's Theorem to KMS weights.