KMS States for generalized Gauge actions on Cuntz-Krieger algebras

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Given a zero-one matrix A we consider certain one-parameter groups of automorphisms of the Cuntz-Krieger algebra \( {\user1{\mathcal{O}}}_{A} \), 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.