Ideals of étale groupoid algebras and Exel's Effros-Hahn conjecture
type: Item
instance of: scholarly article
title: Ideals of étale groupoid algebras and Exel's Effros-Hahn conjecture
DOI: 10.4171/JNCG/423
author: Benjamin Steinberg
published in: Journal of Noncommutative Geometry
publication date: 2022-02-08T00:00:00Z
full work available at URL: https://arxiv.org/abs/1810.10580
review text: Summary: We extend to arbitrary commutative base rings a recent result of Demeneghi that every ideal of an ample groupoid algebra over a field is an intersection of kernels of induced representations from isotropy groups, with a much shorter proof, by using the author's Disintegration Theorem for groupoid representations. We also prove that every primitive ideal is the kernel of an induced representation from an isotropy group; however, we are unable to show, in general, that it is the kernel of an irreducible induced representation. If each isotropy group is finite (e.g., if the groupoid is principal) and if the base ring is Artinian (e.g., a field), then we can show that every primitive ideal is the kernel of an irreducible representation induced from isotropy.
Mathematics Subject Classification ID: 22A22
Mathematics Subject Classification ID: 20M18
Mathematics Subject Classification ID: 20M25
Mathematics Subject Classification ID: 16S36
zbMATH DE Number: 7471130
zbMATH Keywords: étale groupoids
zbMATH Keywords: groupoid algebras
zbMATH Keywords: Effros-Hahn conjecture
Wikidata QID: Q113691978
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7471130