Symmetries of the KMS Simplex

Johannes Christensen

doi:10.1007/s00220-018-3250-5

Symmetries of the KMS Simplex

^*Corresponding author for this work

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11 Citations (Scopus)

Abstract

A continuous groupoid homomorphism c on a locally compact second countable Hausdorff étale groupoid G gives rise to a C^*-dynamical system in which every β-KMS state can be associated to a e^- ^β ^c-quasi-invariant measure μ on G⁽⁰⁾. Letting Δ _μ denote the set of KMS states associated to such a μ, we will prove that Δ _μ is a simplex for a large class of groupoids, and we will show that there is an abelian group that acts transitively and freely on the extremal points of Δ _μ. This abelian group can be described using the support of μ, so our theory can be used to obtain a description of all KMS states by describing the e^- ^β ^c-quasi-invariant measures. To illustrate this we will describe the KMS states for the Cuntz–Krieger algebras of all finite higher rank graphs without sources and a large class of continuous one-parameter groups.

Original language	English
Journal	Communications in Mathematical Physics
Volume	364
Issue	1
Pages (from-to)	357-383
Number of pages	27
ISSN	0010-3616
DOIs	https://doi.org/10.1007/s00220-018-3250-5
Publication status	Published - 1 Nov 2018

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Symmetries of the KMS Simplex

Abstract

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