Abstract
AbstractWe 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 groupoidC*-algebras, we describe the equilibrium states of the cross-sectional algebra in terms of measurable fields of states on theC*-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 groupoidC*-algebras, and then apply this to twistedC*-algebras of strongly connected finitek-graphs.
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