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Journal of Operator Theory

Volume 70, Issue 2, Autumn 2013  pp. 513-530.

KMS states on the $C^*$-algebras of non-principal groupoids

Authors:  Sergey Neshveyev
Author institution: Department of Mathematics, University of Oslo, PO Box 1053 Blindern, N-0316 Oslo, Norway

Summary:  We describe KMS-states on the $C^*$-algebras of etale groupoids in terms of measurable fields of traces on the $C^*$-algebras of the isotropy groups. We use this description to analyze tracial states on the transformation groupoid $C^*$-algebras and to give a short proof of recent results of Cuntz, Deninger and Laca on the Toeplitz algebras of the $ax+b$ semigroups of the rings of integers in number fields.

Keywords:  KMS-states, groupoids, Toeplitz algebras, number fields

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