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

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.

20 pages

Cited by in corpus (2)

• On the Simplicity of C${}^{\ast }$-algebras Associated to Multispinal Groups
• Invariant sets and normal subgroupoids of universal étale groupoids induced by congruences of inverse semigroups