Classification of 5-dimensional restricted Lie algebras over perfect fields, I

TL;DR

This paper extends the classification of 5-dimensional p-nilpotent restricted Lie algebras over perfect fields of characteristic p≥5, building on previous work for lower dimensions using an adapted Skjelbred-Sund method.

Contribution

It provides a complete classification of 5-dimensional p-nilpotent restricted Lie algebras over perfect fields, introducing an adapted classification method.

Findings

Classified all 5-dimensional p-nilpotent restricted Lie algebras over perfect fields.

Extended the Skjelbred-Sund method to this classification.

Built upon prior classifications of lower-dimensional cases.

Abstract

The purpose of this paper is to classify all $p$-nilpotent restricted Lie algebras of dimension 5 over perfect fields of characteristic $p\geq 5$. Our work builds upon the recent work of Schneider and Usefi on the classification of $p$-nilpotent restricted Lie algebras of dimension up to 4 over perfect fields of characteristic $p$. The method we use here to classify $p$-nilpotent restricted Lie algebras is the analogue of Skjelbred-Sund method for classifying nilpotent Lie algebras.