Reconstructing Etale Groupoids from Semigroups
Operator Algebras
2020-09-15 v2 General Topology
Rings and Algebras
Abstract
We unify various \'etale groupoid reconstruction theorems such as: 1) Kumjian-Renault's reconstruction from a groupoid C*-algebra. 2) Exel's reconstruction from an ample inverse semigroup. 3) Steinberg's reconstruction from a groupoid ring. 4) Choi-Gardella-Thiel's reconstruction from a groupoid L^p-algebra. We do this by working with certain bumpy semigroups S of functions defined on an \'etale groupoid G. The semigroup structure of S together with the diagonal subsemigroup D then yields a natural domination relation < on S. The groupoid of <-ultrafilters is then isomorphic to the original groupoid G.
Cite
@article{arxiv.2002.02108,
title = {Reconstructing Etale Groupoids from Semigroups},
author = {Tristan Bice and Lisa Orloff Clark},
journal= {arXiv preprint arXiv:2002.02108},
year = {2020}
}