Relations among invariants of complex filiform Lie algebras.
type: Item
instance of: scholarly article
title: Relations among invariants of complex filiform Lie algebras.
zbMATH Open document ID: 1047.17005
DOI: 10.1016/S0096-3003(02)00673-2
author: D. Massart
published in: Applied Mathematics and Computation
publication date: 2003-11-25T00:00:00Z
review text: In the paper under review, the authors pursue their previous investigation [Algebras Groups Geom. 16, 297--317 (1999; Zbl 1001.17010)] on the classification of complex filiform \(n\)-di\-men\-sion\-al Lie algebras in terms of the invariants \(i\) and \(j\) defined by \[ i=\max\{k\in{\mathbb N}\mid[{\mathcal L}^{n-k+2},{\mathcal L}^2]=\{0\}\} \] and \[ j=\max\{k\in{\mathbb N}\mid[{\mathcal L}^{n-k+1},{\mathcal L}^{n-k+1}]=\{0\}\}, \] where \({\mathcal L}={\mathcal L}^1\supseteq{\mathcal L}^2\supseteq\cdots\) is the descending central sequence of a nilpotent \(n\)-dimensional Lie algebra \({\mathcal L}\). The main results of the present paper give new inequalities that relate the numbers \(i\), \(j\) and \(n\). Thus, Theorem~8 says that \(n\leq2j-3\) provided \(i\neq4\), while Theorem~7 gives a lower bound for \(i+j\). The last section of the paper discusses the classification of filiform Lie algebras with \(j=n-1\).
reviewed by: Daniel Beltiţă
Mathematics Subject Classification ID: 17B30
Mathematics Subject Classification ID: 17B05
zbMATH DE Number: 2009108
zbMATH Keywords: filiform Lie algebra
zbMATH Keywords: invariants
MaRDI profile type: Publication
cites work: Classification des algèbres de Lie nilpotentes complexes de dimension 7. (Classification of nilpotent complex Lie algebras of dimension 7)
cites work: Q4252461
cites work: Q5285437
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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(02)00673-2
OpenAlex ID: W1998617164
description: scientific article; zbMATH DE number 2009108