Abstract

We consider fibrewise singly generated Fell bundles over étale groupoids. Given a continuous realvalued 1cocycle on the groupoid, there is a natural dynamics on the crosssectional algebra of the Fell bundle. We study the KuboMartinSchwinger equilibrium states for this dynamics. Following work of Neshveyev on equilibrium states on groupoid C∗algebras, we describe the equilibrium states of the crosssectional 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 crosssectional 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 kgraphs.