Contributions to real exponential Lie groups
type: Item
instance of: scholarly article
title: Contributions to real exponential Lie groups
zbMATH Open document ID: 0947.22004
author: Martin Moskowitz
author: Michael Wüstner
published in: Monatshefte für Mathematik
publication date: 2000-11-06T00:00:00Z
review text: Necessary and sufficient conditions are given for the exponentiality of real Lie groups of mixed type, i.e. groups which are neither solvable nor semisimple. Necessary conditions are proved in Section 2 for connected real Lie groups to be exponential (Theorems 2 and 3), and sufficient conditions are given for real algebraic groups which are semidirect products of compact connected Lie groups acting on simply connected solvable Lie groups which are exponential themselves (Theorem 4), and also for connected Mal'cev splittable Lie groups satisfying some properties with respect to their Lie algebras (Theorem 5). All conditions deal with the centralizers of ad-nilpotent elements of the corresponding Lie algebras. A ``universal'' counterexample shows at last that all these criteria are not necessary \textit{and} sufficient.
Mathematics Subject Classification ID: 22E15
zbMATH DE Number: 1466225
zbMATH Keywords: exponential mapping
zbMATH Keywords: surjectivity of the exponential mapping
zbMATH Keywords: real Lie groups
zbMATH Keywords: real algebraic groups
zbMATH Keywords: Mal'cev splittable Lie groups
reviewed by: Helmut Boseck
MaRDI profile type: Publication
full work available at URL: s006050050085
OpenAlex ID: W1988379611
Wikidata QID: Q115385669
DOI: 10.1007/S006050050085
description: scientific article; zbMATH DE number 1466225