The algebraic classification of nilpotent commutative algebras

TL;DR

This paper provides a comprehensive algebraic classification of complex 5-dimensional nilpotent commutative algebras, utilizing central extension methods and recent classifications of related algebraic structures.

Contribution

It offers the first complete classification of complex 5-dimensional nilpotent commutative algebras, advancing the understanding of their algebraic structure.

Findings

Complete classification of complex 5-dimensional nilpotent commutative algebras

Development of a classification method based on central extensions

Integration of recent classifications of complex 5-dimensional nilpotent commutative $rak{CD}$-algebras

Abstract

This paper is devoted to the complete algebraic classification of complex $5$-dimensional nilpotent commutative algebras. Our method of classification is based on the standard method of classification of central extensions of smaller nilpotent commutative algebras and the recently obtained classification of complex $5$-dimensional nilpotent commutative $\mathfrak{CD}$-algebras.