Rapid Decay for Principal \'Etale Groupoids
Operator Algebras
2023-07-03 v2 Functional Analysis
Abstract
This work concerns a generalization of property (RD) from discrete groups to twisted \'etale groupoids equipped with a length function. We show that, under the assumption that the \'etale groupoid is principal, twisted property (RD) is equivalent to polynomial growth. This generalizes a result of Chen and Wei concerning rapid decay for metric spaces with bounded geometry. Additionally, some permanence properties of groupoid (RD) are established.
Cite
@article{arxiv.2304.12262,
title = {Rapid Decay for Principal \'Etale Groupoids},
author = {Alex Weygandt},
journal= {arXiv preprint arXiv:2304.12262},
year = {2023}
}
Comments
New version incorporates twists and fixes some typos. Comments welcome