A new method for classifying complex filiform Lie algebras
type: Item
instance of: scholarly article
title: A new method for classifying complex filiform Lie algebras
zbMATH Open document ID: 1021.17010
DOI: 10.1016/S0096-3003(99)00270-2
author: Luis Boza
author: E. M. Fedriani
author: Juan Núñez Valdés
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: The authors propose an alternative computational procedure to classify nilpotent Lie algebras, more concretely those of maximal nilindex, also called filiform following \textit{M. Vergne} [Bull. Soc. Math. Fr. 98, 81-116 (1970; Zbl 0244.17011)]. In contrast to other methods used in the literature, here the authors focus on conditions ensuring that certain transformations of a Lie algebra lead to another element lying in the same orbit. This allows them to predict the number of parametrized families appearing for each fixed dimension (the dimensions \(n\leq 14\) are commented upon at the end of the paper).
Mathematics Subject Classification ID: 17B30
zbMATH DE Number: 1860886
zbMATH Keywords: Lie algebras
zbMATH Keywords: isomorphism
zbMATH Keywords: filiform
reviewed by: Rutwig Campoamor Stursberg
MaRDI profile type: Publication
cites work: Classification of filiform Lie algebras in dimension 8
cites work: Q4324524
cites work: Q4274257
cites work: Low-dimensional filiform Lie algebras
cites work: An algorithm to obtain laws of families of filiform Lie algebras
cites work: Some nilpotent Lie algebras of even dimension
cites work: Cohomologie des algèbres de Lie nilpotentes. Application à l'étude de la variété des algèbres de Lie nilpotentes
full work available at URL: s0096-3003(99)00270-2
OpenAlex ID: W2087311017
description: scientific article; zbMATH DE number 1860886