Equilibrium states on the Toeplitz algebras of small higher-rank graphs

TL;DR

This paper explicitly computes the equilibrium states (KMS states) for dynamical systems derived from Toeplitz algebras of small higher-rank graphs, advancing understanding of operator-algebraic dynamics in graph-based systems.

Contribution

It provides explicit calculations of KMS states for small higher-rank graph Toeplitz algebras, a novel contribution to operator-algebraic dynamical systems.

Findings

Explicit KMS states for graphs with up to four components

Characterization of equilibrium states in small higher-rank graph systems

Advancement in understanding operator-algebraic dynamics

Abstract

We consider a family of operator-algebraic dynamical systems involving the Toeplitz algebras of higher-rank graphs. We explicitly compute the KMS states (equilibrium states) of these systems built from small graphs with up to four connected components.