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QUOTIENTS OF ÉTALE GROUPOIDS AND THE ABELIANIZATIONS OF GROUPOID C*-ALGEBRAS
Published online by Cambridge University Press: 07 April 2020
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 a Cuntz–Krieger uniqueness theorem for a universal groupoid C*-algebra.
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- Research Article
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- Creative Commons
- This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
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- © 2020 Australian Mathematical Publishing Association Inc.
Footnotes
Communicated by L. O. Clark
This work was supported by the RIKEN Junior Research Associate Program.
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