On surjectivity of the power maps of solvable Lie groups
type: Item
instance of: scholarly article
title: On surjectivity of the power maps of solvable Lie groups
zbMATH Open document ID: 0990.22005
author: Pralay Chatterjee
published in: Journal of Algebra
publication date: 2002-06-16T00:00:00Z
review text: Let \(G\) be a connected solvable Lie group. The author finds conditions under which the power map \(P_n: G\to G\), \(P_ng=g^n\), is surjective. The most detailed results are obtained for the case where \(G\) is a semi-direct product of a compact torus and a simply connected solvable exponential group. If \(G\) is simply connected, the surjectivity of \(P_n\) (\(n\geq 2\)) is shown to be equivalent to its injectivity. In this case \(P_n\) is a diffeomorphism. Each of these properties is equivalent to the surjectivity of the exponential map.
Mathematics Subject Classification ID: 22E25
zbMATH DE Number: 1749645
zbMATH Keywords: solvable Lie group
zbMATH Keywords: power map
zbMATH Keywords: exponential map
reviewed by: Anatoly N. Kochubei
MaRDI profile type: Publication
full work available at URL: jabr.2001.9007
OpenAlex ID: W2094162586
Wikidata QID: Q115395686
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DOI: 10.1006/JABR.2001.9007
description: scientific article; zbMATH DE number 1749645