Symmetries of the KMS Simplex
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-βc-quasi-invariant measure μ on G(0). Letting Δμ denote the set of KMS states associated to such a μ, we will prove that Δμ 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 Δμ. 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-βc-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.
- Publication:
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Communications in Mathematical Physics
- Pub Date:
- November 2018
- DOI:
- 10.1007/s00220-018-3250-5
- arXiv:
- arXiv:1710.04412
- Bibcode:
- 2018CMaPh.364..357C
- Keywords:
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- Mathematics - Operator Algebras
- E-Print:
- 25 pages. Some typos and a paragraph in the introduction have been corrected. This is a pre-print of an article to appear in Communications in Mathematical Physics