KMS States for generalized Gauge actions on Cuntz-Krieger algebras(An application of the Ruelle-Perron-Frobenius Theorem)

Given a zero-one matrix A we consider certain one-parameter groups of automorphisms of the Cuntz-Krieger algebra \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\user1{\mathcal{O}}}_{A} $$\end{document}, generalizing the usual gauge group, and depending on a positive continuous function H defined on the Markov space ∑A. The main result consists of an application of Ruelle’s Perron-Frobenius Theorem to show that these automorphism groups admit a single KMS state.