English

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

R2 v1 2026-06-28T10:16:07.688Z