Equivalence of definitions of AF groupoid
We prove the equivalence of two definitions of AF groupoid in the literature: one by Renault and the other by Farsi, Kumjian, Pask and Sims. In both definitions, an AF groupoid is an increasing union of more basic groupoids, called elementary groupoids. Surprisingly, the two definitions of elementary groupoid are not equivalent; they coincide if and only if the local homeomorphism that characterises them is a covering map.
Authors
- Lisa Clark (ORCID: https://orcid.org/0000-0002-1237-4291)
- Camila F. Sehnem (ORCID: https://orcid.org/0000-0002-5007-4230)
- Astrid an Huef (ORCID: https://orcid.org/0000-0003-3301-521X)
- R. Teixeira De Lima (ORCID: https://orcid.org/0000-0001-5545-6513)
Institutions
- University of Waterloo (CA)
- Victoria University of Wellington (NZ)
Publication Details
- Journal
- Proceedings of the American Mathematical Society
- Published
- 2025-01-29
- DOI
- https://doi.org/10.1090/proc/16932
- Primary Topic
- Advanced Operator Algebra Research
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Marsden Fund