On the C*-algebra of a locally injective surjection and its KMS states

TL;DR

This paper investigates the C*-algebra structure associated with locally injective surjections on compact metric spaces, establishing an isomorphism with a related algebra and analyzing KMS states at various inverse temperatures.

Contribution

It introduces a canonical extension making the C*-algebras isomorphic and applies this to study KMS states for generalized gauge actions.

Findings

Existence of a canonical locally homeomorphic extension

Isomorphism between the original and extended C*-algebras

Characterization of inverse temperatures for KMS states

Abstract

It shown that an a locally injective surjection on a compact metric space admits a canonical locally homeomorphic extension such that the associated C*-algebras are isomorphic. This is then used in a study of the possible inverse temperatures of KMS states for a generalized gauge action.