12,000

We have over 12,000 students, from over 100 countries, within one of the safest campuses in the UK

93%

93% of Lancaster students go into work or further study within six months of graduating

Home > Research > Publications & Outputs > On abelian subalgebras and ideals of maximal di...
View graph of relations

« Back

On abelian subalgebras and ideals of maximal dimension in supersolvable Lie algebras

Research output: Contribution to journalJournal article

Published

Journal publication date03/2014
JournalJournal of Pure and Applied Algebra
Journal number3
Volume218
Number of pages16
Pages497-503
Early online date27/07/13
Original languageEnglish

Abstract

In this paper, the main objective is to compare the abelian subalgebras and ideals of maximal dimension for finite-dimensional supersolvable Lie algebras. We characterise the maximal abelian subalgebras of solvable Lie algebras and study solvable Lie algebras containing an abelian subalgebra of codimension 2. Finally, we prove that nilpotent Lie algebras with an abelian subalgebra of codimension 3 contain an abelian ideal with the same dimension, provided that the characteristic of the underlying field is not two. Throughout the paper, we also give several examples to clarify some results.

Bibliographic note

The final, definitive version of this article has been published in the Journal, Journal of Pure and Applied Algebra 218 (3), 2014, © ELSEVIER.