Classification of restricted Lie algebras of dimension $4$

TL;DR

This paper extends the classification of restricted Lie algebras to dimension 4 over algebraically closed fields of positive characteristic, building on prior work for dimensions up to 3.

Contribution

It provides a complete classification of restricted Lie algebras of dimension 4, which was previously unknown.

Findings

Classification of 4-dimensional restricted Lie algebras achieved

Extension of existing classifications from dimension 3 to 4

New structural insights into restricted Lie algebras of higher dimension

Abstract

Restricted Lie algebras of dimension up to $3$ over algebraically closed fields of positive characteristic were classified by Wang and his collaborators in [25, 19]. In this paper, we obtain a classification of restricted Lie algebras of dimension $4$ over such fields.