C-sections of Lie algebras

TL;DR

This paper introduces and studies the concept of c-sections in Lie algebras, revealing their properties and using them to characterize solvable Lie algebras.

Contribution

It defines c-sections of maximal subalgebras in Lie algebras and explores their properties, providing new characterizations of solvability.

Findings

All c-sections are isomorphic.

c-sections relate to c-ideals and ideal index.

New criteria for solvability of Lie algebras.

Abstract

Let $M$ be a maximal subalgebra of a Lie algebra $L$ and $A/B$ a chief factor of $L$ such that $B \subseteq M$ and $A \not \subseteq M$. We call the factor algebra $M \cap A/B$ a $c$-section of $M$. All such $c$-sections are isomorphic, and this concept is related those of $c$-ideals and ideal index previously introduced by the author. Properties of $c$-sections are studied and some new characterizations of solvable Lie algebras are obtained.