Characterising Semi-Simple Lie Algebras by Their Borel Nilpotent Radical

TL;DR

This paper demonstrates that semi-simple Lie algebras can be uniquely characterized by their maximal nilpotent subalgebra, specifically the nilpotent radical of a Borel subalgebra, providing a new perspective on their structure.

Contribution

It introduces a novel characterization of semi-simple Lie algebras through their Borel nilpotent radical, linking algebraic structure to subalgebra properties.

Findings

Semi-simple Lie algebras are characterized by their maximal nilpotent subalgebra.

The nilpotent radical of a Borel subalgebra uniquely determines the Lie algebra.

This characterization offers a new structural insight into semi-simple Lie algebras.

Abstract

We show that semi-simple lie algebras can be characterized by their maximal nilpotent subalgebra, which is the same as the nilpotent radical of a Borel subalgebra.