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

Abstract

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.

12 pages; subsumes the earlier preprint "Traces on crossed products" arXiv:1010.0600; minor correction of the version published in JOT

References in corpus (5)

• On Bost-Connes type systems for number fields
• Bost-Connes systems, Hecke algebras, and induction
• Type III_1 equilibrium states of the Toeplitz algebra of the affine semigroup over the natural numbers
• Von Neumann algebras arising from Bost-Connes type systems
• Traces on crossed products

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• C*-algebras from actions of congruence monoids on rings of algebraic integers
• Ground states of groupoid C*-algebras, phase transitions and arithmetic subalgebras for Hecke algebras
• KMS weights on groupoid and graph C*-algebras
• KMS states on Nica-Toeplitz C*-algebras
• The groupoid approach to equilibrium states on right LCM semigroup C*-algebras
• KMS weights on graph C*-algebras II Factor types and ground states
• Symmetries of the KMS simplex
• Phase transitions on C*-algebras from actions of congruence monoids on rings of algebraic integers
• KMS states on the crossed product $C^{\ast }$-algebra of a homeomorphism
• $C^{\ast }$-algebras of right LCM monoids and their equilibrium states
• Phase transition in O_2
• KMS states on the Toeplitz algebras of higher-rank graphs
• Isotropy fibers of ideals in groupoid C${}^{\ast }$-algebras
• Partition functions as C*-dynamical invariants and actions of congruence monoids
• C*-dynamical invariants and Toeplitz algebras of graphs
• KMS states on the C*-algebras of finite graphs
• KMS states on the C*-algebras of Fell bundles over groupoids
• Spatial realisations of KMS states on the C*-algebras of higher-rank graphs
• KMS spectra for group actions on compact spaces
• (Non)exotic completions of the group algebras of isotropy groups
• A tracial characterization of Furstenberg's $\times p,\times q$ conjecture
• Probabilistic boundaries of finite extensions of quantum groups
• Constructing number field isomorphisms from *-isomorphisms of certain crossed product C*-algebras
• Sheaves of Measures and KMS-Weights on Topological Graph Algebras
• Exact circle maps and KMS states
• Multidimensional Contours à la Fröhlich-Spencer and Boundary Conditions for Quantum Spin Systems
• Cocycles on Certain Groupoids Associated to ${\mathbb{N}}^k$-Actions
• AF $C^{\ast }$-algebras from non AF groupoids
• Tracial weights on topological graph algebras