Dimensionally nilpotent Lie algebras
type: Item
instance of: scholarly article
title: Dimensionally nilpotent Lie algebras
zbMATH Open document ID: 0649.17010
DOI: 10.1016/0021-8693(88)90247-5
author: P. L. Manley
author: George F. Leger
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: An \(n\)-dimensional Lie algebra \(L\) is dimensionally nilpotent if it has a nilpotent derivation \(\Delta\) with \(\Delta^{n-1}\ne 0\). The first of the two theorems in this short paper says that a dimensionally nilpotent Lie algebra over a field of characteristic 0 must either be solvable or be simple of dimension 3. The second theorem pursues the solvable case and presents results regarding a maximal nilpotent ideal in \(L\).
reviewed by: Thomas A. Farmer
Mathematics Subject Classification ID: 17B30
zbMATH DE Number: 4059645
zbMATH Keywords: solvable Lie algebra
zbMATH Keywords: DNL-algebra
zbMATH Keywords: nilpotent derivation
zbMATH Keywords: dimensionally nilpotent Lie algebra
zbMATH Keywords: maximal nilpotent ideal
MaRDI profile type: Publication
full work available at URL: 0021-8693(88)90247-5
OpenAlex ID: W2094793742
Wikidata QID: Q115366348
cites work: Semi-Simple Algebras and Generalized Derivations
cites work: The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group
description: scientific article; zbMATH DE number 4059645