3-BiHom-Lie superalgebras induced by BiHom-Lie superalgebras

ABSTRACT

The purpose of this paper is to study the relationships between a BiHom-Lie superalgebras and its induced 3-BiHom-Lie superalgebras. We introduce the notion of $({\alpha }^s,{\text{β}}^r)$-derivation, $({\alpha }^s,{\text{β}}^r)$-quasiderivation and generalized $({\alpha }^s,{\text{β}}^r)$-derivation of 3-BiHom-Lie superalgebras and their relation with derivation of BiHom-Lie superalgebras. We introduce also the concepts of Rota-Baxter operators and Nijenhuis Operators of 3-BiHom-Lie superalgebras. We also explore the construction of 3-BiHom-Lie superalgebras by using Rota-Baxter of BiHom-Lie superalgebras.

KEYWORDS:

• BiHom-Lie superalgebras
• 3-BiHom-Lie superalgebras
• $\left({\alpha }^s{\text{β}}^r\right)$-derivation
• Rota-Baxter operators
• Nijenhuis operators

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 17A40
• 17B70

Disclosure statement

No potential conflict of interest was reported by the authors.