The algebraic classification of nilpotent commutative $\mathfrak{CD}$-algebras

TL;DR

This paper provides an algebraic classification of complex 5-dimensional nilpotent commutative d-algebras, building on the classification of nilpotent Jordan algebras, to systematically categorize these algebraic structures.

Contribution

It offers the first comprehensive algebraic classification of 5-dimensional nilpotent commutative d-algebras, extending the classification of nilpotent Jordan algebras.

Findings

Complete classification of 5-dimensional nilpotent commutative d-algebras.

Connection established between d-algebras and Jordan algebras.

Framework for future classifications of higher-dimensional cases.

Abstract

An algebraic classification of complex $5$-dimensional nilpotent commutative $\mathfrak{CD}$-algebras is given. This classification is based on an algebraic classification of complex $5$-dimensional nilpotent Jordan algebras.