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arXiv · 2101.08556

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
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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.

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Becky Armstrong, Gilles G. de Castro, Lisa Orloff Clark, Kristin Courtney, Ying-Fen Lin, Kathryn McCormick, Jacqui Ramagge, Aidan Sims, Benjamin Steinberg. 2021-01-21. Reconstruction of twisted Steinberg algebras. https://doi.org/10.1093/imrn%2Frnab291

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