Reconstructing Etale Groupoids from Semigroups

2020/02/06 by Bice, Tristan, Clark, Lisa Orloff · 2 citations
#06F05 #18B40 #20M18 #20M25 #22A22 #46L05 #47D03 #FOS: Mathematics #General Topology (math.GN) #Operator Algebras (math.OA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2002.02108

Abstract

We unify various étale 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 étale groupoid G. The semigroup structure of S together with the diagonal subsemigroup D then yields a natural domination relation < on S. The groupoid of

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• Rigidity of pseudofunction algebras of ample groupoids
• On Graded Quasi-Cartan Pairs and Twisted Steinberg Algebras

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