Some Results about Triangular Representations of Lie Algebras

TL;DR

This paper introduces the concept of triangular representations of Lie algebras, provides a version of Ado's theorem for them, and explores 2-irreducible modules over nonreductive Lie algebras.

Contribution

It presents a new framework for triangular representations, extends Ado's theorem to this context, and analyzes modules over nonreductive Lie algebras.

Findings

Triangular representations are formally defined.

A version of Ado's theorem is established for these representations.

Analysis of 2-irreducible modules over nonreductive Lie algebras.

Abstract

We introduce the concept of a triangular representation of a Lie algebra, give a counterpart of Ado's theorem, and discuss $2$-irreducible triangular modules over a nonreductive Lie algebra.