The Generalized Effros-Hahn Conjecture for Groupoids

TL;DR

This paper proves the generalized Effros-Hahn conjecture for all second countable amenable locally compact Hausdorff groupoids, confirming that primitive ideals are induced from stability groups, thus advancing the understanding of groupoid C*-algebras.

Contribution

The paper establishes the conjecture for a broad class of groupoids, refining previous results and relying on Renault's foundational work.

Findings

Confirmed the conjecture for all second countable amenable groupoids

Connected primitive ideals to stability groups in this context

Sharpened previous theoretical results in the field

Abstract

The generalized Effros-Hahn conjecture for groupoid C*-algebras says that, if G is amenable, then every primitive ideal of the groupoid C*-algebra C*(G) is induced from a stability group. We prove that the conjecture is valid for all second countable amenable locally compact Hausdorff groupoids. Our results are a sharpening of previous work of Jean Renault and depend significantly on his results.