Lie algebras of vector fields and generalized foliations
type: Item
instance of: scholarly article
title: Lie algebras of vector fields and generalized foliations
zbMATH Open document ID: 0841.53027
DOI: 10.5565/PUBLMAT_37293_10
author: J. Grabowski
published in: Publicacions Matemàtiques
publication date: 1996-07-14T00:00:00Z
full work available at URL: https://eudml.org/doc/41534
review text: The author proves a Pursell-Shanks type theorem in the smooth, real-analytic and holomorphic cases. Namely, the following main result is stated: Let \({\mathcal F}_i\) be a finitely generated non-singular foliation on a manifold \(M_i\) and \({\mathcal L}_i \subset{\mathfrak X}(M_i)\) a Lie subalgebra of foliation preserving vector fields, with \(i = 1,2\). If \(\Phi : {\mathcal L}_1 \to {\mathcal L}_2\) is a Lie algebra isomorphism, then \(\Phi = \varphi_*\) for a foliation preserving diffeomorphism \(\varphi : M_1 \to M_2\).
reviewed by: Marco Modugno
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 17B66
zbMATH DE Number: 575442
zbMATH Keywords: Pursell-Shanks type theorem
zbMATH Keywords: foliation
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 575442