Quotients of \'etale groupoids and the abelianizations of groupoid C*-algebras
Abstract
In this paper, we introduce quotients of \'etale 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 \'etale groupoid is implied by the full uniqueness property of its groupoid C*-algebra.
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