On maximal subalgebras of Lie algebras containing Engel subalgebras

TL;DR

This paper investigates the properties of maximal subalgebras of Lie algebras that contain Engel subalgebras, focusing on their influence on the structure of the algebra, especially when these subalgebras have codimension greater than one.

Contribution

It provides new insights into the structure of Lie algebras by analyzing maximal subalgebras containing Engel subalgebras, particularly those with codimension greater than one.

Findings

Characterization of maximal subalgebras containing Engel subalgebras

Analysis of subalgebras with codimension greater than one

Implications for the structure of Lie algebras

Abstract

Relationships between certain properties of maximal subalgebras of a Lie algebra $L$ and the structure of $L$ itself have been studied by a number of authors. Amongst the maximal subalgebras, however, some exert a greater influence on particular results than others. Here we study properties of those maximal subalgebras that contain Engel subalgebras, and of those that also have codimension greater than one in $L$.