KMS States on Generalised Bunce–Deddens Algebras and their Toeplitz Extensions

  title={KMS States on Generalised Bunce–Deddens Algebras and their Toeplitz Extensions},
  author={David Robertson and James Rout and Aidan Sims},
  journal={Bulletin of the Malaysian Mathematical Sciences Society},
We study the generalised Bunce–Deddens algebras and their Toeplitz extensions constructed by Kribs and Solel from a directed graph and a sequence $$\omega $$ω of positive integers. We describe both of these $$C^*$$C∗-algebras in terms of novel universal properties, and prove uniqueness theorems for them; if $$\omega $$ω determines an infinite supernatural number, then no aperiodicity hypothesis is needed in our uniqueness theorem for the generalised Bunce–Deddens algebra. We calculate the KMS… 

Entropy theory for the parametrization of the equilibrium states of Pimsner algebras

Structure and classification of generalised bunce-deddens algebras and their KMS States




Von Neumann algebras of strongly connected higher-rank graphs

We investigate the factor types of the extremal KMS states for the preferred dynamics on the Toeplitz algebra and the Cuntz–Krieger algebra of a strongly connected finite $$k$$k-graph. For inverse

SimpleC*-algebra generated by isometries

AbstractWe consider theC*-algebra $$\mathcal{O}_n $$ generated byn≧2 isometriesS1,...,Sn on an infinite-dimensional Hilbert space, with the property thatS1S*1+...+SnS*n=1. It turns out that

The ideal structure of Cuntz–Krieger algebras

We construct a universal Cuntz–Krieger algebra ${\cal {AO}}_A$, which is isomorphic to the usual Cuntz–Krieger algebra ${\cal O}_A$ when $A$ satisfies condition $(I)$ of Cuntz and Krieger. The Cuntz

A Class of Limit Algebras Associated with Directed Graphs

Abstract Every directed graph defines a Hilbert space and a family of weighted shifts that act on the space. We identify a natural notion of periodicity for such shifts and study their C* -algebras.


We associate to each row-nite directed graph E a universal Cuntz-Krieger C-algebra C(E), and study how the distribution of loops in E aects the structure of C(E) .W e prove that C(E) is AF if and

Partial Dynamical Systems and the KMS Condition

Abstract: Given a countably infinite 0–1 matrix A without identically zero rows, let 𝒪A be the Cuntz–Krieger algebra recently introduced by the authors and 𝒯A be the Toeplitz extension of 𝒪A, once