• Corpus ID: 119326782

The Toeplitz noncommutative solenoid and its KMS states

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



Applications of compact topological graph c*-algebras to noncommutative solenoids

We study the KMS states of the Toeplitz extension of the noncommutative solenoids introduced by Latremoliere and Packer. We demonstrate that noncommutative solenoids cannot be constructed as a direct

KMS states of quasi-free dynamics on Pimsner algebras

Noncommutative solenoids and their projective modules

Let p be prime. A noncommutative p-solenoid is the C*-algebra of Z[1/p] x Z[1/p] twisted by a multiplier of that group, where Z[1/p] is the additive subgroup of the field Q of rational numbers whose

KMS states on C*-algebras associated to local homeomorphisms

For every Hilbert bimodule over a C*-algebra, there are natural gauge actions of the circle on the associated Toeplitz algebra and Cuntz–Pimsner algebra, and hence natural dynamics obtained by

Phase transitions on the Toeplitz algebras of Baumslag-Solitar semigroups

Spielberg has recently shown that Baumslag-Solitar groups associated to pairs of positive integers are quasi-lattice ordered in the sense of Nica. Thus they have tractable Toeplitz algebras. Each of

Boundary quotients of the Toeplitz algebra of the affine semigroup over the natural numbers

Abstract We study the Toeplitz algebra 𝒯(ℕ⋊ℕ×) and three quotients of this algebra: the C*-algebra 𝒬ℕ recently introduced by Cuntz, and two new ones, which we call the additive and multiplicative

The Toeplitz algebra of a Hilbert bimodule

Suppose a C*-algebra A acts by adjointable operators on a Hilbert A-module X. Pimsner constructed a C*-algebra O_X which includes, for particular choices of X, crossed products of A by Z, the Cuntz

Hecke algebras, type III factors and phase transitions with spontaneous symmetry breaking in number theory

In this paper, we construct a naturalC*-dynamical system whose partition function is the Riemann ζ function. Our construction is general and associates to an inclusion of rings (under a suitable