On simple $15$-dimensional Lie algebras in characteristic $2$

TL;DR

This paper explores the structure and classification of 15-dimensional simple Lie algebras over algebraically closed fields of characteristic 2, contributing to the broader understanding of Lie algebra classification in this setting.

Contribution

It provides new insights into the structure of 15-dimensional simple Lie algebras in characteristic 2, advancing classification efforts in this area.

Findings

Identification of specific properties of 15-dimensional simple Lie algebras in characteristic 2

Progress towards classification of these algebras

Clarification of their structural features

Abstract

Motivated by the recent progress towards classification of simple finite-dimensional Lie algebras over an algebraically closed field of characteristic $2$, we investigate such $15$-dimensional algebras.