8-dimensional 2-step nilpotent Lie algebras over algebraically closed fields of char $\ne 2, 3$

TL;DR

This paper classifies 8-dimensional 2-step nilpotent Lie algebras over algebraically closed fields with characteristic not 2 or 3 using elementary linear algebra and geometric methods.

Contribution

It provides a self-contained, elementary classification of these Lie algebras, extending previous geometric approaches with simpler linear algebra techniques.

Findings

Complete classification of 8-dimensional 2-step nilpotent Lie algebras

Uses elementary linear algebra and geometric arguments

Applicable over algebraically closed fields with char ≠ 2,3

Abstract

We provide a self contained, elementary, and geometrically-flavored classification of $8$-dimensional $2$-step nilpotent Lie algebras over algebraically closed fields of characteristic $\ne 2,3$, using the algebro-geometric arguments from \cite{B} and elementary linear algebra.