Angelic way for modular Lie algebras toward Kim's conjecture

TL;DR

This paper investigates the structure of classical modular Lie algebras over fields with characteristic at least 7, aiming to prove they are Park's Lie algebras and thus Hypo-Lie algebras, contributing to Kim's conjecture.

Contribution

It provides a proof that classical modular Lie algebras of types C_l and A_l are Park's Lie algebras, supporting Kim's conjecture.

Findings

Classical modular Lie algebras of types C_l and A_l are Park's Lie algebras.

Supports the hypothesis that these algebras are Hypo-Lie algebras.

Advances understanding of modular Lie algebra classification.

Abstract

We consider modular Lie algebras over algebraically closed field of characteristic $p \geq 7$. This paper purports to prove the conjecture that classical modular Lie algebras,in particular of $C_l$ and of $A_l$ type, should be a Park's Lie algebra, and so a Hypo- Lie algebra.