KMS states on the Toeplitz algebras of higher-rank graphs

Abstract

The Toeplitz algebra TC⁎(Λ) for a finite k-graph Λ is equipped with a continuous one-parameter group αr for each r∈Rk, obtained by composing the map R∋t→(eitr1,…,eitrk)∈Tk with the gauge action on TC⁎(Λ). In this paper we give a complete description of the β-KMS states for the C⁎-dynamical system (TC⁎(Λ),αr) for all finite k-graphs Λ and all values of β∈R and r∈Rk.