# The Toeplitz noncommutative solenoid and its KMS states

@article{Brownlowe2016TheTN, title={The Toeplitz noncommutative solenoid and its KMS states}, author={Nathan Brownlowe and Mitchel Hawkins and Aidan Sims}, journal={arXiv: Operator Algebras}, year={2016} }

We use Katsura's topological graphs to define Toeplitz extensions of Latr\'emoli\`ere and Packer's noncommutative-solenoid C*-algebras. We identify a natural dynamics on each Toeplitz noncommutative solenoid and study the associated KMS states. Our main result shows that the space of extreme points of the KMS simplex of the Toeplitz noncommutative torus at a strictly positive inverse temperature is homeomorphic to a solenoid; indeed, there is an action of the solenoid group on the Toeplitz…

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