PreprintCC BY 4.0arXiv
Some étale groupoids as groupoids of fractions
Abstract
Given a monoid that can be embedded in a group and that acts partially on a set, we show that under certain conditions the category associated with the partial action has a groupoid of fractions. By imposing some topological conditions on the action, we show that the groupoid is actually étale. This étale groupoid arises naturally in C∗-algebra theory.
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BibTeX
@misc{lawson2026some,
title = {{Some étale groupoids as groupoids of fractions}},
author = {Mark V. Lawson},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34813},
eprint = {2609.34813},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34813},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Some étale groupoids as groupoids of fractions
AU - Mark V. Lawson
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34813
UR - https://arxiv.org/abs/2609.34813
AB - Given a monoid that can be embedded in a group and that acts partially on a set, we show that under certain conditions the category associated with the partial action has a groupoid of fractions. By imposing some topological conditions on the action, we show that the groupoid is actually étale. This étale groupoid arises naturally in C^∗-algebra theory.
ER -