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

Towers, David (2022) Abelian subalgebras and ideals of maximal dimension in supersolvable and nilpotent Lie algebras. Linear and Multilinear Algebra, 70 (13). pp. 2551-2568. ISSN 0308-1087

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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 char- acteristic of the field is greater than five.