Equilibrium states on higher-rank Toeplitz non-commutative solenoids

Authors

Zahra Afsar, University of SydneyFollow
Astrid An Huef, Victoria University of WellingtonFollow
Iain F. Raeburn, Victoria University of WellingtonFollow
Aidan Sims, University of WollongongFollow

RIS ID

135431

Publication Details

Afsar, Z., An Huef, A., Raeburn, I. & Sims, A. (2019). Equilibrium states on higher-rank Toeplitz non-commutative solenoids. Ergodic Theory and Dynamical Systems, Online First 1-32.

Abstract

We consider a family of higher-dimensional non-commutative tori, which are twisted analogues of the algebras of continuous functions on ordinary tori and their Toeplitz extensions. Just as solenoids are inverse limits of tori, our Toeplitz non-commutative solenoids are direct limits of the Toeplitz extensions of non-commutative tori. We consider natural dynamics on these Toeplitz algebras, and we compute the equilibrium states for these dynamics. We find a large simplex of equilibrium states at each positive inverse temperature, parametrized by the probability measures on an (ordinary) solenoid.

Grant Number

ARC/DP180100595