KMS States for generalized Gauge actions on Cuntz-Krieger algebras

(An application of the Ruelle-Perron-Frobenius Theorem)
Original Paper

DOI: 10.1007/s00574-004-0001-3

Cite this article as:
Exel*, R. Bull Braz Math Soc, New Series (2004) 35: 1. doi:10.1007/s00574-004-0001-3

Abstract.

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.

Keywords:

C*-algebrasCuntz-Krieger algebrasKMS statesgauge actionRuelle-Perron-Frobenius Theorem

Mathematical subject classification:

46L5537A55

Copyright information

© Sociedade Brasileira de Matemática 2004

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidade Federal de Santa CatarinaFlorianópolis SCBrazil