KMS states on the Toeplitz algebras of higher-rank graphs

Abstract

The Toeplitz algebra $\mathcal{T}{C}^{\ast }(\Lambda )$ for a finite $k$-graph $\Lambda$ is equipped with a continuous one-parameter group ${\alpha }^r$ for each $r\in {\mathbb{R}}^k$, obtained by composing the map $\mathbb{R}\ni t\to (e^{it{r}_1},\dots ,e^{it{r}_k})\in {\mathbb{T}}^k$ with the gauge action on $\mathcal{T}{C}^{\ast }(\Lambda )$. In this paper we give a complete description of the $\beta$-KMS states for the $C^{\ast }$-dynamical system $(\mathcal{T}{C}^{\ast }(\Lambda ),{\alpha }^r)$ for all finite $k$-graphs $\Lambda$ and all values of $\beta \in \mathbb{R}$ and $r\in {\mathbb{R}}^k$.

36 pages. Comments and questions are warmly welcomed at [email protected]

References in corpus (1)

• Groupoid models for the C*-algebras of topological higher-rank graphs

Cited by in corpus (1)

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