Reconstruction of Twisted Steinberg Algebras. (16th November 2021)

• Record Type: Journal Article
• Authors: Armstrong, Becky; de Castro, Gilles G; Clark, Lisa Orloff; Courtney, Kristin; Lin, Ying-Fen; McCormick, Kathryn; Ramagge, Jacqui; Sims, Aidan; Steinberg, Benjamin
• Is Part Of: International mathematics research notices. Volume 2023:Number 3(2023)
• Page Start: 2474
• Page End: 2542
• Publication Date: 2021-11-16
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnab291
• Languages: English
• ISSNs: 1073-7928

Abstract

Abstract: We show how to recover a discrete twist over an ample Hausdorff groupoid from a pair consisting of an algebra and what we call a quasi-Cartan subalgebra . We identify precisely which twists arise in this way (namely, those that satisfy the local bisection hypothesis ), and we prove that the assignment of twisted Steinberg algebras to such twists and our construction of a twist from a quasi-Cartan pair are mutually inverse. We identify the algebraic pairs that correspond to effective groupoids and to principal groupoids. We also indicate the scope of our results by identifying large classes of twists for which the local bisection hypothesis holds automatically.