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 the latter is seen as a Cuntz-Pimsner algebra, as recently shown by Szymanski. We study the KMS equilibrium states of C*-dynamical systems based on OA and TA, with dynamics satisfying σt(sx) = Nxit sx for the canonical generating partial isometries sx and arbitrary real numbers Nx > 1. The KMSβ states on both OA and TA are completely characterized for certain values of the inverse temperature β, according to the position of β relative to three critical values, defined to be the abscissa of convergence of certain Dirichlet series associated to A and the N(x). Our results for OA are derived from those for TA by virtue of the former being a covariant quotient of the latter. When the matrix A is finite, these results give theorems of Olesen and Pedersen for On and of Enomoto, Fujii and Watatani for OA as particular cases.
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