The Toeplitz noncommutative solenoid and its KMS states
Nathan Brownlowe, Mitchell Hawkins and Aidan Sims
Abstract
We use Katsura's topological graphs to define Toeplitz
extensions of Latrémolière and Packer's
noncommutative-solenoid -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 noncommutative solenoid that induces a free and
transitive action on the extreme boundary of the KMS simplex.
With the exception of the degenerate case of trivial rotations,
at inverse temperature zero there is a unique KMS state, and
only this one factors through Latrémolière and
Packer's noncommutative solenoid.
AMS Subject Classification:
Primary 46L55.