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arXiv · 2406.12866

Skew-supersymmetric solution of the super Malcev Yang-Baxter equation and Pre-Malcev superalgebras

Fattoum Harrathi
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Abstract

The purpose of this paper is to introduce the notion of pre-Malcev superalgebras as the algebraic structure behind the super $\mathcal{O}$-operators on Malcev superalgebras. Moreover, the relations among Malcev superalgebras, pre-Malcev superalgebras and pre-alternative superalgebras are established. Then, we study the operator forms of the classical Yang-Baxter equation (CYBE) in Malcev superalgebras and give their relationship with super $\mathcal{O}$-operators. There are close relationships between the CYBE in Malcev superalgebras and pre-Malcev superalgebras which can be interpreted through the super $\mathcal{O}$-operators.

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Fattoum Harrathi. 2024-03-22. Skew-supersymmetric solution of the super Malcev Yang-Baxter equation and Pre-Malcev superalgebras. https://arxiv.org/abs/2406.12866

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