Indice des sous-alg\`ebres biparaboliques d'une alg\`ebre de Lie simple classique

TL;DR

This paper introduces a reduction algorithm to compute the index of seaweed subalgebras in classical simple Lie algebras, enabling the identification of Frobenius Lie algebras and expanding understanding of their structure.

Contribution

It generalizes previous results by providing a new algorithm for calculating indices of seaweed subalgebras in classical Lie algebras, leading to new examples of Frobenius Lie algebras.

Findings

Computed indices for various families of seaweed subalgebras

Identified new classes of Frobenius Lie algebras

Extended the applicability of index calculation methods

Abstract

We generalize the results in [2] giving a reduction algorithm allowing to compute the index of seaweed subalgebras of classical simple Lie algebras. We thus are able to obtain the index of some interesting families of seaweed subalgebras and to give new examples of large classes of Frobenius Lie algebras among them.