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arXiv · 1905.04518

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

Abdelkader Ben Hassine·Sami Mabrouk·Othmen Ncib
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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.

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Abdelkader Ben Hassine, Sami Mabrouk, Othmen Ncib. 2019-05-11. $3$-BiHom-Lie superalgebras induced by BiHom-Lie superalgebras. https://doi.org/10.1080/03081087.2020.1713040

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