Modularity and distributivity in the subideal lattice of a Lie algebra
type: Item
instance of: scholarly article
title: Modularity and distributivity in the subideal lattice of a Lie algebra
zbMATH Open document ID: 0568.17003
author: Alexander Lashkhi
author: Irene A. M. Zimmermann
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/107975
review text: This article gives necessary and sufficient conditions for the subideal lattice of a finite-dimensional Lie algebra over a field of characteristic zero to be (1) modular and (2) distributive. A Lie algebra \(L\) for which the relation of being an ideal in \(L\) is transitive is called a \({\mathcal T}\)-Lie algebra. Equivalent conditions for the subideal lattice of such an algebra to be distributive are derived.
Mathematics Subject Classification ID: 17B05
zbMATH DE Number: 3906684
zbMATH Keywords: modular lattice
zbMATH Keywords: distributive lattice
zbMATH Keywords: transitive Lie algebra
zbMATH Keywords: subideal lattice
zbMATH Keywords: finite-dimensional Lie algebra
zbMATH Keywords: characteristic zero
MaRDI profile type: Publication
cites work: Q4055834
cites work: Q5532570
cites work: Q5525438
cites work: Q5510907
cites work: Q5736170
cites work: A Theory of Subinvariant Lie Algebras
description: scientific article; zbMATH DE number 3906684