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

TL;DR

This paper studies KMS states for generalized gauge actions on Cuntz-Krieger algebras, applying Ruelle's Perron-Frobenius Theorem to establish the existence of a unique KMS state for these automorphisms.

Contribution

It introduces a class of automorphism groups on Cuntz-Krieger algebras depending on a continuous function and proves the existence of a unique KMS state using Ruelle's theorem.

Findings

Existence of a unique KMS state for the generalized gauge automorphisms.

Application of Ruelle's Perron-Frobenius Theorem to operator algebras.

Extension of gauge actions to more general settings.

Abstract

Given a zero-one matrix A we consider certain one-parameter groups of automorphisms of the Cuntz-Krieger algebra O_A, generalizing the usual gauge group, and depending on a positive continuous function H defined on the Markov space \Sigma_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.