Hom-Novikov algebras

TL;DR

This paper introduces Hom-Novikov algebras, a twisted generalization of Novikov algebras, explores their construction from various algebraic structures, and explicitly classifies endomorphisms for low-dimensional cases.

Contribution

It defines Hom-Novikov algebras, shows how to derive them from Novikov algebras via twisting, and constructs new classes from Hom-commutative and Hom-Lie algebras.

Findings

Explicit classification of endomorphisms for 2- and 3-dimensional Novikov algebras

Construction of Hom-Novikov algebras from Hom-commutative algebras with derivations

Construction of Hom-Novikov algebras from Hom-Lie algebras

Abstract

We study a twisted generalization of Novikov algebras, called Hom-Novikov algebras, in which the two defining identities are twisted by a linear map. It is shown that Hom-Novikov algebras can be obtained from Novikov algebras by twisting along any algebra endomorphism. All algebra endomorphisms on complex Novikov algebras of dimensions two or three are computed, and their associated Hom-Novikov algebras are described explicitly. Another class of Hom-Novikov algebras is constructed from Hom-commutative algebras together with a derivation, generalizing a construction due to Dorfman and Gel'fand. Two other classes of Hom-Novikov algebras are constructed from Hom-Lie algebras together with a suitable linear endomorphism, generalizing a construction due to Bai and Meng.