C-Ideals of Lie Algebras

TL;DR

This paper introduces the concept of c-ideals in Lie algebras, explores their properties, and uses them to characterize solvable and supersolvable Lie algebras, including classification of certain Lie algebras.

Contribution

It defines c-ideals in Lie algebras, studies their properties, and provides new characterizations and classifications related to solvability and supersolvability.

Findings

Characterization of solvable Lie algebras using c-ideals

Classification of Lie algebras where all 1-dimensional subalgebras are c-ideals

Properties of c-ideals analogous to c-normal subgroups

Abstract

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