2002/06/07 by R. Exel, Exel, R., Artur O. Lopes +2
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Operator Algebra Research #Computability, Logic, AI Algorithms #Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA) #math.DS #math.OA
paper · pdf · doi:10.48550/arxiv.math/0206074
The statement of Theorem 9.10 was reformulated to include a missing hypothesis and some references were added
openalex publication_date 2002/06/07 · arxiv created 2002/07/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.