Groupoid C*-algebras with Hausdorff Spectrum

2012/07/28 by Geoff Goehle, Goehle, Geoff
Mathematics · #22A22 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1207.6715

openalex publication_date 2012/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose G is a second countable, locally compact Hausdorff groupoid with abelian stabilizer subgroups and a Haar system. We provide necessary and sufficient conditions for the groupoid C^*-algebra to have Hausdorff spectrum. In particular we show that the spectrum of C^*(G) is Hausdorff if and only if the stabilizers vary continuously with respect to the Fell topology, the orbit space G⁽⁰⁾/G is Hausdorff, and, given convergent sequences χ_i→ χ and γ_i⋅χ_i → ω in the dual stabilizer groupoid S where the γ_i∈ G act via conjugation, if χ and ω are elements of the same fiber then χ= ω

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