# Normalization of a nonlinear representation of a Lie algebra, regular on an abelian ideal

## TL;DR

This paper develops a normalization method for nonlinear Lie algebra representations that are regular on an abelian ideal, extending previous work to a broader class of representations.

## Contribution

It introduces a generalized normal form for nonlinear Lie algebra representations regular on an abelian ideal, expanding the theoretical framework beyond prior models.

## Key findings

- Defined a new normal form for nonlinear Lie algebra representations
- Extended normalization techniques to representations regular on abelian ideals
- Provided theoretical foundations for further applications in Lie algebra analysis

## Abstract

We consider a nonlinear representation of a Lie algebra which is regular on an abelian ideal, we define a normal form which generalizes that defined in [D. Arnal, M. Ben Ammar, M. Selmi, {\rm Normalisation d'une repr\'esentation non lin\'eaire d'une alg\`ebre de Lie}. {\it Annales de la Facult\'e des Sciences de Toulouse}, 5e s\'erie, tome 9, No 3, 1988, p 355--379.]