# Sur l'indice des sous-alg\`ebres biparaboliques de $\mathfrak{gl}(n)$

## TL;DR

This paper investigates the index of seaweed subalgebras in the complex Lie algebra rak{gl}(n), deriving formulas and identifying new Frobenius Lie algebras.

## Contribution

It provides new formulas for the index of certain seaweed subalgebras and introduces new families of Frobenius Lie algebras.

## Key findings

- Formulas for the index of specific seaweed subalgebras
- Identification of new Frobenius Lie algebra families
- Properties that facilitate index computation

## Abstract

We give some properties on the index of seaweed subalgebras of the complex Lie algebra $\mathfrak{gl}(n)$ which allow to obtain formulas for the index of some interesting classes of this family and to give new families of Frobenius Lie algebras.