Twisting $\mathcal{O}$-operators by $(2,3)$-Cocycle of Hom-Lie-Yamaguti Algebras with Representations
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908245313978368 |
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| author | Mabrouk, Sami Silvestrov, Sergei Zouaidi, Fatma |
| author_facet | Mabrouk, Sami Silvestrov, Sergei Zouaidi, Fatma |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18804 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Twisting $\mathcal{O}$-operators by $(2,3)$-Cocycle of Hom-Lie-Yamaguti Algebras with Representations Mabrouk, Sami Silvestrov, Sergei Zouaidi, Fatma Rings and Algebras Mathematical Physics Quantum Algebra 17B61, 17D30, 17A40, 17B10, 17B56 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. |
| title | Twisting $\mathcal{O}$-operators by $(2,3)$-Cocycle of Hom-Lie-Yamaguti Algebras with Representations |
| topic | Rings and Algebras Mathematical Physics Quantum Algebra 17B61, 17D30, 17A40, 17B10, 17B56 |
| url | https://arxiv.org/abs/2502.18804 |