C*-algebras, approximately proper equivalence relations and thermodynamic formalism

AUTOR(ES)

Exel, Ruy

DATA DE PUBLICAÇÃO

2011

RESUMO

We introduce a non-commutative generalization of the notion of (approximately proper) equivalence relations 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 thermodynamicswe prove that these states are unique as well. We also show a relationship between maximizing measures (the analogue of the Aubry–Mathermeasures for expanding maps) and ground states. In the last section we explore an interesting example of phase transitions.

ASSUNTO(S)

c* algebras termodinamica análise matemática : espaço de hausdorff : estado kms

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