The primitive spectrum of C*-algebras of etale groupoids with abelian isotropy

2024/05/03 by Johannes Christensen, Sergey Neshveyev, Christensen, Johannes +1
Mathematics · Computer Science · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Advanced Algebra and Logic

paper · pdf · doi:10.48550/arxiv.2405.02025

Abstract

Given a Hausdorff locally compact étale groupoid \mathcal G, we describe as a topological space the part of the primitive spectrum of C^*(\mathcal G) obtained by inducing one-dimensional representations of amenable isotropy groups of \mathcal G. When \mathcal G is amenable, second countable, with abelian isotropy groups, our result gives the description of Prim C^*(\mathcal G) conjectured by van Wyk and Williams. This, in principle, completely determines the ideal structure of a large class of separable C^*-algebras, including the transformation group C^*-algebras defined by amenable actions of discrete groups with abelian stabilizers and the C^*-algebras of higher rank graphs.

Related

• The ideal structure of C*-algebras of etale groupoids with isotropy groups of local polynomial growth
• The primitive ideals of some étale groupoid C*-algebras
• The Primitive Ideal Space of Groupoid C*-Algebras for Groupoids with Abelian Isotropy
• Isotropy fibers of ideals in groupoid C^*-algebras
• Simplicity criteria for etale groupoid C^*-algebras