The construction and deformation of BiHom-Novikov agebras

TL;DR

This paper introduces BiHom-Novikov algebras, constructs new classes from existing algebraic structures, and develops their deformation theory, revealing their associative and nilpotent properties.

Contribution

It constructs two classes of BiHom-Novikov algebras from BiHom-commutative algebras and Rota-Baxter operators, and develops their deformation theory.

Findings

Quadratic BiHom-Novikov algebras are associative.

Sub-adjacent BiHom-Lie algebras are 2-step nilpotent.

Developed 1-parameter formal deformation theory.

Abstract

BiHom-Novikov agebra is a generalized Hom-Novikov algebra endowed with two commuting multiplicative linear maps. The main purpose of this paper is to show that two classes of BiHom-Novikov algebras can be constructed from BiHom-commutative algebras together with derivations and BiHom-Novikov algebras with Rota-Baxter operators, respectively. We show that quadratic BiHom-Novikov algebras are associative algebras and the sub-adjacent BiHom-Lie algebras of BiHom-Novikov algebras are 2-step nilpotent. Moreover, we develop the 1-parameter formal deformation theory of BiHom-Novikov algebras.