• DOI:10.1017/S0305004119000379
• Corpus ID: 119655932

KMS states on the C*-algebras of Fell bundles over groupoids

@article{Afsar2017KMSSO,
  title={KMS states on the C*-algebras of Fell bundles over groupoids},
  author={Zahra Afsar and Aidan Sims},
  journal={Mathematical Proceedings of the Cambridge Philosophical Society},
  year={2017},
  volume={170},
  pages={221 - 246}
}

• Zahra Afsar, A. Sims
• Published 2 August 2017
• Mathematics
• Mathematical Proceedings of the Cambridge Philosophical Society

Abstract We consider fibrewise singly generated Fell bundles over étale groupoids. Given a continuous real-valued 1-cocycle on the groupoid, there is a natural dynamics on the cross-sectional algebra of the Fell bundle. We study the Kubo–Martin–Schwinger equilibrium states for this dynamics. Following work of Neshveyev on equilibrium states on groupoid C*-algebras, we describe the equilibrium states of the cross-sectional algebra in terms of measurable fields of states on the C*-algebras of the restrictions of the Fell bundle to the isotropy subgroups of the groupoid. As a special case, we obtain a description of the trace space of the cross-sectional algebra. We apply our result to generalise Neshveyev’s main theorem to twisted groupoid C*-algebras, and then apply this to twisted C*-algebras of strongly connected finite k-graphs.