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.

中文翻译：

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KMS 状态关于群上 Fell 丛的 C*-代数

我们考虑在 étale groupoids 上单独生成的 Fell 束。给定群上的一个连续实值 1-cocycle，在 Fell 丛的横截面代数上有一个自然动力学。我们研究了这种动力学的 Kubo-Martin-Schwinger 平衡状态。跟随 Neshveyev 关于群上平衡状态的工作C*-代数，我们用可测量的状态场来描述横截面代数的平衡状态C*-Fell 丛对群样的各向同性子群的限制的代数。作为一个特例，我们得到了截面代数的迹空间的描述。我们应用我们的结果将 Neshveyev 的主要定理推广到扭曲的群C*-代数，然后将其应用于扭曲C*-强连通有限代数ķ-图表。