# $3$-BiHom-Lie superalgebras induced by BiHom-Lie superalgebras

## TL;DR

This paper explores the relationships between BiHom-Lie superalgebras and their induced 3-BiHom-Lie superalgebras, introducing new derivation concepts and operators, and constructing 3-BiHom-Lie superalgebras via Rota-Baxter operators.

## Contribution

It introduces new derivation notions, Rota-Baxter and Nijenhuis operators for 3-BiHom-Lie superalgebras, and constructs these algebras from BiHom-Lie superalgebras.

## Key findings

- Defined $( ext{α}^s, ext{β}^r)$-derivations and quasiderivations.
- Established relations between derivations of BiHom-Lie and 3-BiHom-Lie superalgebras.
- Constructed 3-BiHom-Lie superalgebras using Rota-Baxter operators.

## 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 $(\alpha^s,\beta^r)$-derivation, $(\alpha^s,\beta^r)$-quasiderivation and generalized $(\alpha^s,\beta^r)$-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 BiHom $3$-Lie superalgebras. We also explore the construction of $3$-BiHom-Lie superalgebras by using Rota-Baxter of BiHom-Lie superalgebras.