# The algebraic and geometric classification of nilpotent binary Lie algebras

## TL;DR

This paper provides a comprehensive algebraic and geometric classification of nilpotent binary Lie algebras up to dimension 6 over various fields, including applications to related algebraic structures.

## Contribution

It offers the first complete algebraic and geometric classification of nilpotent binary Lie algebras of dimension up to 6 over arbitrary fields and over complex numbers.

## Key findings

- Classification of nilpotent binary Lie algebras of dimension ≤6 over any field of characteristic not 2.
- Complete geometric classification of 6-dimensional nilpotent binary Lie algebras over complex numbers.
- Application to classify nilpotent anticommutative algebras of dimension .

## Abstract

The paper is devoted to give the complete algebraic classification of nilpotent binary Lie algebras of dimension $\leq 6$ over an arbitrary base field ${\mathbb{F}}$ of characteristic not $2$ and the complete geometric classification of nilpotent binary Lie algebras of dimension $6$ over $\mathbb C.$ As an application, we have the algebraic and geometric classification of nilpotent anticommutative $\mathfrak{CD}$-algebras of dimension $\leq 6.$