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Equilibrium states on higher-rank Toeplitz non-commutative solenoids

Journal Article


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.

UOW Authors


  •   Afsar, Zahra (external author)
  •   An Huef, Astrid (external author)
  •   Raeburn, Iain F. (external author)
  •   Sims, Aidan

Publication Date


  • 2019

Citation


  • 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.

Scopus Eid


  • 2-s2.0-85065257385

Number Of Pages


  • 31

Start Page


  • 1

End Page


  • 32

Volume


  • Online First

Place Of Publication


  • United Kingdom

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.

UOW Authors


  •   Afsar, Zahra (external author)
  •   An Huef, Astrid (external author)
  •   Raeburn, Iain F. (external author)
  •   Sims, Aidan

Publication Date


  • 2019

Citation


  • 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.

Scopus Eid


  • 2-s2.0-85065257385

Number Of Pages


  • 31

Start Page


  • 1

End Page


  • 32

Volume


  • Online First

Place Of Publication


  • United Kingdom