The nil radical for Lie or anti-Lie triple systems
type: Item
instance of: scholarly article
title: The nil radical for Lie or anti-Lie triple systems
zbMATH Open document ID: 0790.17002
author: Noriaki Kamiya
published in: Journal of Algebra
publication date: 1993-08-17T00:00:00Z
review text: The author introduces and investigates a nil radical (the maximal nilpotent ideal) for Lie and anti-Lie triple systems. The notion of powers of an ideal introduced here is not the straightforward generalization of the Lie algebra case one might expect, and therefore the ensuring notion of nilpotency is stronger than for Lie algebras. The following seems to provide a counterexample to Theorem 7 (which states that \([R,T,T]\subset N\) for the Lister solvable radical \(R\) and the nilradical \(N\) of the Lie triple system \(T\)): Let \(L\) be a semisimple Lie algebra, \(M\) an irreducible \(L\)-module and \(T\) the Lie triple system built from the split null extension \(L+M\). Then \(R=M\), \(N=0\) (by the author's definition) yet \([R,T,T]=R\).
Mathematics Subject Classification ID: 17A40
Mathematics Subject Classification ID: 17B60
zbMATH DE Number: 218577
zbMATH Keywords: Lie triple system
zbMATH Keywords: solvable radical
zbMATH Keywords: nil radical
zbMATH Keywords: anti-Lie triple systems
reviewed by: S Walcher
Wikidata QID: Q115396303
MaRDI profile type: Publication
full work available at URL: jabr.1993.1131
OpenAlex ID: W2017891259
DOI: 10.1006/JABR.1993.1131
description: scientific article; zbMATH DE number 218577