2000/06/22 by Ruy Exel, Exel, Ruy, Marcelo Laca +1 · 1 citation
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods for differential equations #Operator Algebras (math.OA) #math-ph #math.DS #math.MP #math.OA
paper · pdf · doi:10.48550/arxiv.math/0006169
Plain TeX, 48 pages
arxiv created 2000/06/22 · openalex publication_date 2000/06/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 KMSβstates on both OA and TA are completely characterized for certain values of the inverse temperature β, according to the position of βrelative 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.