Weak c-ideals of Lie algebras

TL;DR

This paper introduces the concept of weak c-ideals in Lie algebras, explores their properties, and uses them to characterize solvable and supersolvable Lie algebras, highlighting the significance of one-dimensional weak c-ideals.

Contribution

It defines weak c-ideals in Lie algebras and provides characterizations of solvability and supersolvability based on these ideals.

Findings

Weak c-ideals have specific properties that relate to the structure of Lie algebras.

One-dimensional weak c-ideals are actually c-ideals.

The paper characterizes solvable and supersolvable Lie algebras using weak c-ideals.

Abstract

A subalgebra B of a Lie algebra L is called a weak c-ideal of L if there is a subideal C of L such that L = B+C and B\cap C \subseteq B_L where B_L is the largest ideal of L contained in B. This is analogous to the concept of weakly c- normal subgroups, which has been studied by a number of authors. We obtain some properties of weak c-ideals and use them to give some characterisations of solvable and supersolvable Lie algebras. We also note that one-dimensional weak c-ideals are c-ideals.