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

Abdelkader Ben Hassine; Sami Mabrouk; Othmen Ncib

doi:10.1080/03081087.2020.1713040

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

Rings and Algebras 2020-03-18 v1

Authors: 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.

Keywords

bihom-lie superalgebra 3-bihom-lie superalgebra derivation rota-baxter operator nijenhuis operator quasiderivation

Cite

@article{arxiv.1905.04518,
  title  = {$3$-BiHom-Lie superalgebras induced by BiHom-Lie superalgebras},
  author = {Abdelkader Ben Hassine and Sami Mabrouk and Othmen Ncib},
  journal= {arXiv preprint arXiv:1905.04518},
  year   = {2020}
}

Comments

arXiv admin note: text overlap with arXiv:1509.03948, arXiv:1601.02356, arXiv:1306.1990 by other authors

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

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