Equivalence of definitions of AF groupoid
Operator Algebras
2023-09-08 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2309.03413,
title = {Equivalence of definitions of AF groupoid},
author = {Lisa Orloff Clark and Astrid an Huef and Rafael P. Lima and Camila F. Sehnem},
journal= {arXiv preprint arXiv:2309.03413},
year = {2023}
}
Comments
11 pages