On nilpotent Lie algebras having a torus of derivations
type: Item
instance of: scholarly article
title: On nilpotent Lie algebras having a torus of derivations
zbMATH Open document ID: 0823.17009
DOI: 10.1007/BF02567448
author: Michel Goze
author: You Hakimjanov
published in: Manuscripta Mathematica
publication date: 1995-01-24T00:00:00Z
full work available at URL: https://eudml.org/doc/155982
review text: Let \({\mathfrak g}\) be a complex nilpotent Lie algebra of dimension \(n\). For \(x \in {\mathfrak g} - [{\mathfrak g}, {\mathfrak g}]\) let \(c(x)\) be the set of dimensions of Jordan blocks of ad \(x\) in decreasing order. Let \(c({\mathfrak g}) = \text{Sup} (c(x),x \in {\mathfrak g} - [{\mathfrak g}, {\mathfrak g}])\) (relative to the lexicographical order). Then \({\mathfrak g}\) is said to be filiform if \(c ({\mathfrak g})\) is maximal, i.e., \((n - 1,1)\). The authors classify the filiform Lie algebras admitting a nonzero diagonalizable derivation. Then, in a section on characteristically nilpotent algebras (i.e., algebras with all derivations nilpotent), they prove that for dimensions greater than 8 any algebraic irreducible component of the variety of complex nilpotent filiform laws of Lie algebras contains an open set whose elements are characteristically nilpotent laws.
Mathematics Subject Classification ID: 17B30
Mathematics Subject Classification ID: 17B40
zbMATH DE Number: 701157
zbMATH Keywords: complex nilpotent Lie algebra
zbMATH Keywords: filiform Lie algebras
zbMATH Keywords: derivation
zbMATH Keywords: characteristically nilpotent algebras
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 701157