The construction and deformation of Hom-Novikov superalgebras

TL;DR

This paper introduces Hom-Novikov superalgebras, explores their construction from other algebraic structures, and develops their deformation theory, revealing their associative and nilpotent properties.

Contribution

It presents new constructions of Hom-Novikov superalgebras and develops their formal deformation theory, expanding understanding of their algebraic structure.

Findings

Hom-Novikov superalgebras can be constructed from Hom-supercommutative algebras with derivations.

Quadratic Hom-Novikov superalgebras are Hom-associative superalgebras.

Hom-Novikov superalgebras have 2-step nilpotent Hom-Lie sub-adjacent algebras.

Abstract

We study a twisted generalization of Novikov superalgebras, called Hom-Novikov superalgebras. It is shown that two classes of Hom-Novikov superalgebras can be constructed from Hom-supercommutative algebras together with derivations and Hom-Novikov superalgebras with Rota-Baxter operators, respectively. We show that quadratic Hom-Novikov superalgebras are Hom-associative superalgebras and the sub-adjacent Hom-Lie superalgebras of Hom-Novikov superalgebras are 2-step nilpotent. Moreover, we develop the 1-parameter formal deformation theory of Hom-Novikov superalgebras.