Equilibrium states on higher-rank Toeplitz non-commutative solenoids. (November 2020)

• Record Type: Journal Article
• Authors: AFSAR, ZAHRA; AN HUEF, ASTRID; RAEBURN, IAIN; SIMS, AIDAN
• Is Part Of: Ergodic theory and dynamical systems. Volume 40:Number 11(2020)
• Page Start: 2881
• Page End: 2912
• Publication Date: 2020-11
• Subjects: 46L05, -- 46L30, -- 46L55; KMS states, -- C∗ -algebras, -- direct limit, -- Toeplitz algebra; Ergodic theory -- Periodicals; Differentiable dynamical systems -- Periodicals; 515.42
• DOI: 10.1017/etds.2019.20
• Languages: English
• ISSNs: 0143-3857

Abstract

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.