Solvable Complemented Lie Algebras

TL;DR

This paper characterizes solvable complemented Lie algebras, showing they decompose into abelian subalgebras and form a specific algebraic class with well-understood ideal structures.

Contribution

It provides a new characterization of solvable complemented Lie algebras and describes their decomposition and ideal properties in detail.

Findings

Decomposition into abelian subalgebras

Formation with residual as ideal closure of prefrattini subalgebras

Nice relation between ideals and decomposition

Abstract

In this paper a characterisation is given of solvable complemented Lie algebras. They decompose as a direct sum of abelian subalgebras and their ideals relate nicely to this decomposition. The class of such algebras is shown to be a formation whose residual is the ideal closure of the prefrattini subalgebras.