Classification of Novikov algebras

TL;DR

This paper develops a classification method for Novikov algebras based on their associated Lie algebras and applies it to classify 3-dimensional Novikov algebras over R and C, and certain 4-dimensional cases over C.

Contribution

It introduces a new classification approach for Novikov algebras and provides comprehensive classifications for specific low-dimensional cases.

Findings

Classified all 3-dimensional Novikov algebras over R and C.

Classified 4-dimensional Novikov algebras over C with nilpotent associated Lie algebra.

Included a list of all 4-dimensional commutative associative algebras over C.

Abstract

We describe a method for classifying the Novikov algebras with a given associated Lie algebra. Subsequently we give the classification of the Novikov algebras of dimension 3 over R and C, as well as the classification of the 4-dimensional Novikov algebras over C whose associated Lie algebra is nilpotent. In particular this includes a list of all 4-dimensional commutative associative algebras over C.