On Lie algebras of vector fields on smooth orbifolds
type: Item
instance of: scholarly article
title: On Lie algebras of vector fields on smooth orbifolds
zbMATH Open document ID: 0617.58002
author: Kōjun Abe
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1986-01-01T00:00:00Z
review text: A paracompact Hausdorff space B is called an orbifold if an open covering \(\{U_ i\}\) of B closed under intersections exists such that for each \(U_ i\), there is an action of a finite group \(\Gamma_ i\) on an open subset \(V_ i\) of \({\mathbb{R}}^ n\) and homeomorphisms \(\Phi_ i: U_ i\to V_ i/\Gamma_ i\) satisfying the obvious compatibility conditions on the intersections \(U_ i\cap U_ j\). The author introduces the Lie algebra \({\mathcal D}(B)\) (\({\mathcal X}(B))\) of smooth vector fields on orbifolds and proves that the Lie algebra isomorphisms \({\mathcal D}(B)\to {\mathcal D}(B')\) (\({\mathcal X}(B)\to {\mathcal X}(B'))\) are in one-to-one correspondence with the diffeomorphisms \(B\to B'\) between orbifolds. The fibered orbifolds and the fiber preserving vector fields are investigated also.
Mathematics Subject Classification ID: 58A99
Mathematics Subject Classification ID: 58C99
Mathematics Subject Classification ID: 57R25
zbMATH DE Number: 4001018
zbMATH Keywords: vector fields
zbMATH Keywords: maximal ideals
zbMATH Keywords: fibered orbifolds
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195177845
OpenAlex ID: W2050444337
cites work: Pursell-Shanks type theorem for orbit spaces of G-manifolds
cites work: Lifting isotopies from orbit spaces
cites work: On Lie Algebras of Vector Fields
cites work: Q4173983
cites work: Infinite dimensional Lie transformation groups
cites work: The Gauss-Bonnet theorem for \(V\)-manifolds
cites work: Lifting smooth homotopies of orbit spaces
cites work: Local Contractions and a Theorem of Poincare
DOI: 10.2977/PRIMS/1195177845
description: scientific article; zbMATH DE number 4001018