CCR and GCR Groupoid C*-algebras

2005/11/17 by Lisa Orloff Clark, Clark, Lisa Orloff
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.math/0511449

openalex publication_date 2005/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose G is a second countable, locally compact, Hausdorff groupoid with a fixed left Haar system. Let \go/G denote the orbit space of G and C^*(G) denote the groupoid C^*-algebra. Suppose that the isotropy groups of G are amenable. We show that C^*(G) is CCR if and only if \go/G is a T₁ topological space and all of the isotropy groups are CCR. We also show that C^*(G) is GCR if and only if \go/G is a T₀ topological space and all of the isotropy groups are GCR.

Related

• Classifying the Type of Principal Groupoid C*-algebras
• The orbit spaces of groupoids whose C^*-algebras are CCR
• The orbit space of groupoids whose C^*-algebras are GCR
• The representation theory of C*-algebras associated to groupoids
• Groupoid C*-algebras with Hausdorff Spectrum