Isotropy fibers of ideals in groupoid C^*-algebras

2023/08/21 by Johannes Christensen, Sergey Neshveyev, Christensen, Johannes +1 · 3 citations
Mathematics · #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.2308.10768

openalex publication_date 2023/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a locally compact étale groupoid and an ideal I in its groupoid C^*-algebra, we show that I defines a family of ideals in group C^*-algebras of the isotropy groups and then study to which extent I is determined by this family. As an application we obtain the following results: (a) prove that every proper ideal is contained in an induced primitive ideal; (b) describe the maximal ideals; (c) classify the primitive ideals for a class of graded groupoids with essentially central isotropy.

Cited by

• On dense subalgebras of the singular ideal in groupoid C*-algebras
• Characterizations of zero singular ideal in étale groupoid C*-algebras via compressible maps
• Examples of non-amenable, boundary-amenable dynamical systems

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