Alg\`ebres de Lie quasi-r\'eductives

TL;DR

This paper investigates a class of algebraic Lie algebras characterized by having a reductive generic stabilizer in the coadjoint action, contributing to the understanding of their structural properties.

Contribution

It introduces and analyzes quasi-reductive algebraic Lie algebras, expanding the classification and understanding of their coadjoint representations.

Findings

Identification of conditions for quasi-reductivity in algebraic Lie algebras

Characterization of the generic stabilizer in coadjoint actions

Insights into the structure of algebraic Lie algebras with reductive stabilizers

Abstract

We study the class of algebraic Lie algebras for which the generic stabilizer of the coadjoint action is reductive modulo the center.