KMS states on the C*-algebras of Fell bundles over groupoids. (19th March 2021)

• Record Type: Journal Article
• Authors: AFSAR, ZAHRA; SIMS, AIDAN
• Is Part Of: Mathematical proceedings of the Cambridge Philosophical Society. Volume 170:Part 2(2021)
• Page Start: 221
• Page End: 246
• Publication Date: 2021-03-19
• Subjects: 46L05, -- 46L55; Mathematics -- Periodicals; 510.5
• DOI: 10.1017/S0305004119000379
• Languages: English
• ISSNs: 0305-0041

Abstract

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.