Reconstruction of Twisted Steinberg Algebras

Becky Armstrong, Gilles G. de Castro, Lisa Orloff Clark*, Kristin Courtney, Ying-Fen Lin, Kathryn McCormick, Jacqui Ramagge, Aidan Sims, Benjamin Steinberg

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish
Number of pages47
JournalInternational Mathematics Research Notices
Early online date16 Nov 2021
DOIs
Publication statusEarly online date - 16 Nov 2021

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