Noncommutative Novikov algebras

TL;DR

This paper explores a broader class of Novikov algebras derived from noncommutative associative algebras with derivations, extending classical understanding of these nonassociative structures.

Contribution

It introduces and studies noncommutative Novikov algebras obtained from noncommutative associative algebras with derivations, generalizing the classical commutative case.

Findings

Characterization of noncommutative Novikov algebras

Extension of classical Novikov algebra constructions

New examples from noncommutative associative algebras

Abstract

The class of Novikov algebras is a popular object of study among classical nonassociative algebras. The generic example of a Novikov algebra may be obtained from a differential associative and commutative algebra. We consider a more general class of linear algebras which may be obtained in the same way from not necessarily commutative associative algebras with a derivation.