# Equilibrium and ground states from Cayley graphs

## TL;DR

This paper investigates the equilibrium states of generalized gauge actions on the $C^*$-algebra of Cayley graphs, providing comprehensive results for nilpotent groups and partial insights for all finitely generated groups.

## Contribution

It offers new analysis of KMS states on Cayley graph $C^*$-algebras, especially advancing understanding for nilpotent groups.

## Key findings

- Complete characterization of KMS states for nilpotent groups
- Partial results for finitely generated groups
- Insights into ground states and $KMS_{ extinfty}$ states

## Abstract

We study the KMS states and $KMS_{\infty}$ states of generalized gauge actions on the $C^*$-algebra of a pointed Cayley graph. Our results provide information for any finitely generated group, but they are only complete for nilpotent groups.