Quotients of étale groupoids and the abelianizations of groupoid C*-algebras

2018/12/18 by Fuyuta Komura, Komura, Fuyuta
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1812.07194

openalex publication_date 2018/12/18 · openalex created_date 2018/12/22 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce quotients of étale groupoids. Using the notion of quotients, we describe the abelianizations of groupoid C*-algebras. As another application, we obtain a simple proof that effectiveness of an étale groupoid is implied by the full uniqueness property of its groupoid C*-algebra.

Citations

• Étale groupoids and their C^*-algebras

Related

• Étale groupoids and their C^*-algebras
• C*-algebras of groupoid morphisms
• *-homomorphisms between groupoid C*-algebras
• Simplicity criteria for etale groupoid C^*-algebras
• Semi etale groupoids and applications