The Primitive Ideal Space of Groupoid C*-Algebras for Groupoids with Abelian Isotropy

2021/08/04 by Daniel W. van Wyk, van Wyk, Daniel W., Dana P. Williams +1
Mathematics · #46L05 #46L55 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2108.02277

openalex publication_date 2021/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the topology of the primitive ideal space of groupoid C*-algebras for groupoids with abelian isotropy. Our results include the known results for action groupoids with abelian stabilizers. Furthermore, we obtain complete results when the isotropy map is continuous except for jump discontinuities, and also when G is a unit space fixing extension of a proper groupoid by an abelian group bundle. We hope that our methods will be a springboard to further results of this type.

Related

• Isotropy fibers of ideals in groupoid C^*-algebras
• The primitive spectrum of C*-algebras of etale groupoids with abelian isotropy
• The primitive ideals of some étale groupoid C*-algebras
• *-homomorphisms between groupoid C*-algebras
• The ideal structure of C*-algebras of etale groupoids with isotropy groups of local polynomial growth