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

Journal Article


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.

Publication Date


  • 2021

Citation


  • Afsar, Z., & Sims, A. (2021). KMS states on the C¿-algebras of Fell bundles over groupoids. Mathematical Proceedings of the Cambridge Philosophical Society, 170(2), 221-246. doi:10.1017/S0305004119000379

Scopus Eid


  • 2-s2.0-85101833361

Web Of Science Accession Number


Start Page


  • 221

End Page


  • 246

Volume


  • 170

Issue


  • 2

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.

Publication Date


  • 2021

Citation


  • Afsar, Z., & Sims, A. (2021). KMS states on the C¿-algebras of Fell bundles over groupoids. Mathematical Proceedings of the Cambridge Philosophical Society, 170(2), 221-246. doi:10.1017/S0305004119000379

Scopus Eid


  • 2-s2.0-85101833361

Web Of Science Accession Number


Start Page


  • 221

End Page


  • 246

Volume


  • 170

Issue


  • 2