Reconstruction of twisted Steinberg algebras
Date
2023
Authors
Armstrong, B.
de Castro, G.G.
Clark, L.O.
Courtney, K.
Lin, Y.F.
McCormick, K.
Ramagge, J.
Sims, A.
Steinberg, B.
Editors
Advisors
Journal Title
Journal ISSN
Volume Title
Type:
Journal article
Citation
International Mathematics Research Notices (IMRN), 2023; 2023(3):2474-2542
Statement of Responsibility
Conference Name
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.
School/Discipline
Dissertation Note
Provenance
Description
Link to a related website: https://unpaywall.org/10.1093/imrn/rnab291, Open Access via Unpaywall
Access Status
Rights
Copyright 2021 The author(s). Published by Oxford University Press.