The algebraic and geometric classification of nilpotent binary and mono Leibniz algebras

TL;DR

This paper provides a comprehensive algebraic and geometric classification of certain complex nilpotent Leibniz algebras, specifically binary and mono types, and derives classifications for related algebraic structures.

Contribution

It offers the first complete algebraic and geometric classification of 5-dimensional binary and 4-dimensional mono nilpotent Leibniz algebras, including related nilpotent algebras.

Findings

Classification of 5-dimensional binary nilpotent Leibniz algebras

Classification of 4-dimensional mono nilpotent Leibniz algebras

Complete classification of 4-dimensional nilpotent algebras of nil-index 3

Abstract

This paper is devoted to the complete algebraic and geometric classification of complex $5$-dimensional nilpotent binary Leibniz and $4$-dimensional nilpotent mono Leibniz algebras. As a corollary, we have the complete algebraic and geometric classification of complex $4$-dimensional nilpotent algebras of nil-index $3$.