A short construction of the Lie algebra $G_2(K)$ over fields $K$ of characteristic $2$

TL;DR

This paper presents a straightforward and elementary construction of the 14-dimensional Lie algebra of type G_2 over fields with characteristic 2, using minimal linear algebra tools.

Contribution

It provides an explicit, simple construction of G_2(K) Lie algebras over characteristic 2 fields, avoiding complex algebraic techniques.

Findings

Explicit construction of G_2(K) in characteristic 2

Uses minimal linear algebra concepts

Simplifies understanding of G_2 over such fields

Abstract

The purpose of this paper is to give an explicit and elementary construction for the Lie algebras of type $G_2(K)$ of dimension 14, over the field K of characteristic 2. We say an elementary construction on the account that we use not more than little naive linear algebra notions.