In this section

Some results regarding the ideal structure of C*-algebras of étale groupoids

Brix, K. A., Carlsen, T. M. and Sims, A. (2024) Some results regarding the ideal structure of C*-algebras of étale groupoids. Journal of the London Mathematical Society, 109(3), e12870. (doi: 10.1112/jlms.12870)

[img] Text
316431.pdf - Published Version
Available under License Creative Commons Attribution.
252kB

Abstract

We prove a sandwiching lemma for inner-exact locally compact Hausdorff étale groupoids. Our lemma says that every ideal of the reduced C*-algebra of such a groupoid is sandwiched between the ideals associated to two uniquely defined open invariant subsets of the unit space. We obtain a bijection between ideals of the reduced C*-algebra, and triples consisting of two nested open invariant sets and an ideal in the C*-algebra of the subquotient they determine that has trivial intersection with the diagonal subalgebra and full support. We then introduce a generalisation to groupoids of Ara and Lolk's relative strong topological freeness condition for partial actions, and prove that the reduced C*-algebras of inner-exact locally compact Hausdorff étale groupoids satisfying this condition admit an obstruction ideal in Ara and Lolk's sense.

Item Type:Articles
Additional Information:This research was supported by Australian Research Council grant DP200100155. KAB acknowledges the support of the Carlsberg Foundation via an Internationalisation Fellowship and the support of the Independent Research Fund Denmark (Case number 1025-00004B).
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Brix, Dr Kevin
Authors: Brix, K. A., Carlsen, T. M., and Sims, A.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of the London Mathematical Society
Publisher:Wiley
ISSN:0024-6107
ISSN (Online):1469-7750
Published Online:20 February 2024
Copyright Holders:Copyright © 2024 The Authors
First Published:First published in Journal of the London Mathematical Society 109(3):e12870
Publisher Policy:Reproduced under a Creative Commons licence

University Staff: Request a correction | Enlighten Editors: Update this record

Deposit and Record Details