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arXiv · 2502.18804

Twisting $\mathcal{O}$-operators by $(2,3)$-Cocycle of Hom-Lie-Yamaguti Algebras with Representations

Sami Mabrouk·Sergei Silvestrov·Fatma Zouaidi
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Abstract

In this paper, we first introduce the notion of twisted $\mathcal O$-operators on a Hom-Lie-Yamaguti algebra by a given $(2,3)$-cocycle with coefficients in a representation. We show that a twisted $\mathcal O$-operator induces a Hom-Lie-Yamaguti structure. We also introduce the notion of a weighted Reynolds operator on a Hom-Lie-Yamaguti algebra, which can serve as a special case of twisted $\mathcal O$-operators on Hom-Lie-Yamaguti algebras. Then, we define a cohomology of twisted $\mathcal O$-operator on Hom-Lie-Yamaguiti algebras with coefficients in a representation. Furthermore, we introduce and study the Hom-NS-Lie-Yamaguti algebras as the underlying structure of the twisted $\mathcal O$-operator on Hom-Lie-Yamaguti algebras. Finally, we investigate the twisted $\mathcal O$-operator on Hom-Lie-Yamaguti algebras induced by the twisted $\mathcal O$-operator on a Hom-Lie algebras.

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BibTeXRIS

Sami Mabrouk, Sergei Silvestrov, Fatma Zouaidi. 2025-02-26. Twisting $\mathcal{O}$-operators by $(2,3)$-Cocycle of Hom-Lie-Yamaguti Algebras with Representations. https://arxiv.org/abs/2502.18804

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