Some results regarding the ideal structure of C*-algebras of étale groupoids
Publication Name
Journal of the London Mathematical Society
Abstract
We prove a sandwiching lemma for inner-exact locally compact Hausdorff étale groupoids. Our lemma says that every ideal of the reduced (Formula presented.) -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 (Formula presented.) -algebra, and triples consisting of two nested open invariant sets and an ideal in the (Formula presented.) -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 (Formula presented.) -algebras of inner-exact locally compact Hausdorff étale groupoids satisfying this condition admit an obstruction ideal in Ara and Lolk's sense.
Open Access Status
This publication may be available as open access
Volume
109
Issue
3
Article Number
e12870
Funding Number
DP200100155
Funding Sponsor
Australian Research Council