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

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  19 November 2019

ZAHRA AFSAR  and
AIDAN SIMS
ZAHRA AFSAR
Affiliation:
Quadrangle, Camperdown Campus, University of Sydney, A14, L4.45, City Road, Sydney, NSW 2006, Australia e-mail: zahra.afsar@sydney.edu.au
AIDAN SIMS
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, 39C. 195, Northfields Avenue, Wollongong, NSW 2522, Australia. e-mail: asims@uow.edu.au
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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.

MSC classification

Primary: 46L05: General theory of $C^*$-algebras
Secondary: 46L55: Noncommutative dynamical systems
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 170 , Issue 2 , March 2021 , pp. 221 - 246
Copyright
© Cambridge Philosophical Society 2019

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