Abelian subalgebras and ideals of maximal dimension in supersolvable and nilpotent lie algebras

ABSTRACT

In this paper, we continue the study of abelian subalgebras and ideals of maximal dimension for finite-dimensional supersolvable and nilpotent Lie algebras. We show that supersolvable 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, and that the same is true for nilpotent Lie algebras with an abelian subalgebra of codimension 4, provided that the characteristic of the field is greater than five.

KEYWORDS:

• Lie algebras
• abelian subalgebra
• abelian ideal
• solvable
• supersolvable
• nilpotent

MATHEMATICS SUBJECT CLASSIFICATIONS 2020:

• 17B05
• 17B20
• 17B30
• 17B50

Disclosure statement

No potential conflict of interest was reported by the authors.