On I-null Lie algebras

TL;DR

This paper studies I-null Lie algebras, characterized by a zero Koszul 3-form, including quotients of Borel subalgebras of semi-simple Lie algebras, and classifies certain nilpotent Lie algebras by Kac-Moody type.

Contribution

It characterizes I-null Lie algebras and provides a classification of low-dimensional indecomposable nilpotent Lie algebras by Kac-Moody type.

Findings

I-null Lie algebras include all quotients of Borel subalgebras of semi-simple Lie algebras.

A classification list of nilpotent Lie algebras of dimension up to 7 by Kac-Moody type.

The paper establishes the structure of I-null Lie algebras in relation to semi-simple and nilpotent cases.

Abstract

We consider the class of Lie algebras for which the Koszul 3-form is zero, and prove that it contains all quotients of Borel subalgebras, or of their nilradicals, of finite dimensional semi-simple Lie algebras. A list of Kac-Moody types for indecomposable nilpotent Lie algebras of dimension at most 7 is given.