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Equilibrium states on higher-rank Toeplitz non-commutative solenoids

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  17 April 2019

ZAHRA AFSAR Open the ORCID record for ZAHRA AFSAR [Opens in a new window] ,
ASTRID AN HUEF Open the ORCID record for ASTRID AN HUEF [Opens in a new window] ,
IAIN RAEBURN Open the ORCID record for IAIN RAEBURN [Opens in a new window]  and
AIDAN SIMS Open the ORCID record for AIDAN SIMS [Opens in a new window]
ZAHRA AFSAR
Affiliation:
School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia email zahra.afsar@sydney.edu.au
ASTRID AN HUEF
Affiliation:
School of Mathematics and Statistics, Victoria University of Wellington, PO Box 600, Wellington6140, New Zealand email astrid.anhuef@vuw.ac.nz, iain.raeburn@vuw.ac.nz
IAIN RAEBURN
Affiliation:
School of Mathematics and Statistics, Victoria University of Wellington, PO Box 600, Wellington6140, New Zealand email astrid.anhuef@vuw.ac.nz, iain.raeburn@vuw.ac.nz
AIDAN SIMS
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia email asims@uow.edu.au
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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.

Keywords

KMS statesC∗ -algebrasdirect limitToeplitz algebra

MSC classification

Primary: 46L05: General theory of $C^*$-algebras 46L30: States 46L55: Noncommutative dynamical systems
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 40 , Issue 11 , November 2020 , pp. 2881 - 2912
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Copyright
© Cambridge University Press, 2019

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