C*-Algebras, Approximately Proper Equivalence Relations, and Thermodynamic Formalism
Operator Algebras
2007-05-23 v2 Dynamical Systems
Abstract
We introduce a non-commutative generalization of the notion of (approximately proper) equivalence relation and propose the construction of a "quotient space". We then consider certain one-parameter groups of automorphisms of the resulting C*-algebra and prove the existence of KMS states at every temperature. In a model originating from Thermodynamics we prove that these states are unique as well. We also show a relationship between maximizing measures (the analogue of the Aubry-Mather measures for expanding maps) and ground states. In the last section we explore an interesting example of phase transitions.
Keywords
Cite
@article{arxiv.math/0206074,
title = {C*-Algebras, Approximately Proper Equivalence Relations, and Thermodynamic Formalism},
author = {R. Exel and A. Lopes},
journal= {arXiv preprint arXiv:math/0206074},
year = {2007}
}
Comments
The statement of Theorem 9.10 was reformulated to include a missing hypothesis and some references were added