The algebraic classification of nilpotent algebras

TL;DR

This paper provides a comprehensive algebraic classification of all complex 4-dimensional nilpotent algebras, identifying 234 isomorphism classes including 66 previously unknown.

Contribution

It offers the first complete classification of complex 4-dimensional nilpotent algebras, adding 66 new algebraic structures to the literature.

Findings

234 isomorphism classes identified

66 new nilpotent algebras discovered

Complete classification achieved

Abstract

We give the complete algebraic classification of all complex 4-dimensional nilpotent algebras. The final list has 234 (parametric families of) isomorphism classes of algebras, 66 of which are new in the literature.