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arXiv · 2312.16543

Yang-Baxter equations and $\mathcal O$-operators of a Hom-Jordan superalgebra with representation

Sami Mabrouk·Othmen Ncib·Sihem Sendi
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Abstract

In this paper, first we recall the notion of Hom-Jordan superalgebras and study their representations. We define the Yang-Baxter equation in a Hom-Jordan superalgebra. Additionally, we extend the connections between $\mathcal {O}$-operators and skew-symmetric solutions Yang-Baxter equation of Hom-Jordan superalgebras (HJYBE). In which, we prove that a super skew-symmetric solution of HJYBE can be interpreted as an $\mathcal{O}$-operator associated to the coadjoint representation. Finally, we study the relationship between Hom-pre-Jordan superalgebras and Hom-Jordan superalgebras via an $\mathcal{O}$-operators. Some other related results are considered.

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Sami Mabrouk, Othmen Ncib, Sihem Sendi. 2023-12-27. Yang-Baxter equations and $\mathcal O$-operators of a Hom-Jordan superalgebra with representation. https://arxiv.org/abs/2312.16543

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