On the structure of maximal solvable extensions and of Levi extensions of nilpotent algebras

TL;DR

This paper provides new bounds on the dimensions of solvable Lie algebras with a fixed nilpotent nilradical and explores restrictions on Levi factors in Levi decomposable algebras, offering insights into their structure and classification.

Contribution

It introduces improved upper estimates for the dimension of solvable algebras with a given nilradical and analyzes restrictions on Levi factors based on characteristic ideals, enhancing understanding of algebra structures.

Findings

Established tighter upper bounds on solvable algebra dimensions

Identified structural restrictions on Levi factors from characteristic ideals

Revised classification perspectives for Levi decomposable algebras up to dimension 9

Abstract

We establish an improved upper estimate on dimension of any solvable algebra s with its nilradical isomorphic to a given nilpotent Lie algebra n. Next we consider Levi decomposable algebras with a given nilradical n and investigate restrictions on possible Levi factors originating from the structure of characteristic ideals of n. We present a new perspective on Turkowski's classification of Levi decomposable algebras up to dimension 9.