Reconstruction of Twisted Steinberg Algebras
Publication Name
International Mathematics Research Notices
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.
Open Access Status
This publication may be available as open access
Volume
2023
Issue
3
First Page
2474
Last Page
2542
Funding Number
88887.368595/2019-00
Funding Sponsor
Horizon 2020 Framework Programme