KMS states on the \(C^*\)-algebras of non-principal groupoids.(English)Zbl 1299.46067
The problem of classifying KMS-states for various \(C^*\)-dynamical systems has been extensively studied since the 1970s. This note consists of three sections.
Section 1. KMS states on groupoid \(C^*\)-algebras. It contains the main general results.
In Section 2, it is explained how to transform groupoids and tracial states on crossed products by abelian groups completely to a measure-theoretic problem.
In Section 3, the Toeplitz algebras of the \(ax+b\) semigroups of the rings of integrals in number fields, recently studied byJ. Cuntz,C. Deninger andM. Laca [Math. Ann. 355, No. 4, 1383–1423 (2013;Zbl 1273.22008),arxiv:1105.5352] on the Toeplitz algebras is considered.
Section 1. KMS states on groupoid \(C^*\)-algebras. It contains the main general results.
In Section 2, it is explained how to transform groupoids and tracial states on crossed products by abelian groups completely to a measure-theoretic problem.
In Section 3, the Toeplitz algebras of the \(ax+b\) semigroups of the rings of integrals in number fields, recently studied byJ. Cuntz,C. Deninger andM. Laca [Math. Ann. 355, No. 4, 1383–1423 (2013;Zbl 1273.22008),arxiv:1105.5352] on the Toeplitz algebras is considered.
Reviewer: Victor Sharapov (Dayton)
MSC:
| 46L30 | States of selfadjoint operator algebras |
| 46L55 | Noncommutative dynamical systems |
| 22D25 | \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations |
