Abelian ideals of maximal dimension for solvable Lie algebras
type: Item
instance of: scholarly article
zbMATH Open document ID: 1257.17015
author: Dietrich Burde
author: Manuel Ceballos
publication date: 2012-08-24T00:00:00Z
full work available at URL: https://arxiv.org/abs/0911.2995
full work available at URL: jlt22031.htm
Mathematics Subject Classification ID: 17B30
Mathematics Subject Classification ID: 17D25
Mathematics Subject Classification ID: 17B50
zbMATH DE Number: 6072205
zbMATH Keywords: abelian subalgebras
zbMATH Keywords: abelian ideals
MaRDI profile type: Publication
arXiv ID: 0911.2995
arXiv classification: math.RA
title: Abelian ideals of maximal dimension for solvable Lie algebras
published in: Journal of Lie Theory
review text: The authors compare the maximal dimensions of abelian subalgebras and abelian ideals for finite dimensional Lie algebras \(L\). Let \(\alpha(L)\) be the former and \(\beta(L)\) be the latter. There is a large literature on these invariants and the authors present an excellent review. In particular they list \(\alpha(L)\) for the complex simple Lie algebras and note the remarkable fact that \(\alpha(L)=\beta(B)\) where \(B\) is a Borel subalgebra of \(L\). They show another remarkable fact: \(\alpha(L)=\beta(L)\) for any solvable Lie algebra over an algebraically closed field of characteristic 0. When the abelian subalgebra has codimension 1, the ideal is constructed explicitly. Also, \(\alpha(L)\) is determined for each indecomposable nilpotent \(L\) of dimension \(\leq 7\), the case of dimension 7 being new.
reviewed by: Ernest L. Stitzinger
description: scientific article; zbMATH DE number 6072205