Extended $\mathcal{O}$-operators, Novikov Yang-Baxter equations and post-Novikov algebras
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908380705062912 |
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| author | Yu, Jianfeng Hong, Yanyong |
| author_facet | Yu, Jianfeng Hong, Yanyong |
| contents | In this paper, we introduce the definition of extended $\mathcal{O}$-operators on a Novikov algebra $(A,\circ)$ associated to an $A$-bimodule Novikov algebra which is a generalization of the definition of $\mathcal{O}$-operators and show that there are new Novikov algebra structures on the $A$-bimodule Novikov algebra obtained from extended $\mathcal{O}$-operators. We also introduce the definition of post-Novikov algebras and show that there is a close relationship between post-Novikov algebras and $\mathcal{O}$-operators of weight $λ$. The tensor form of extended $\mathcal{O}$-operators is also investigated which leads to the definition of extended Novikov Yang-Baxter equations, which is a generalization of the notion of Novikov Yang-Baxter equations. The relationships between extended $\mathcal{O}$-operators, Novikov Yang-Baxter equations, extended Novikov Yang-Baxter equations and generalized Novikov Yang-Baxter equations are established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_20735 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extended $\mathcal{O}$-operators, Novikov Yang-Baxter equations and post-Novikov algebras Yu, Jianfeng Hong, Yanyong Rings and Algebras In this paper, we introduce the definition of extended $\mathcal{O}$-operators on a Novikov algebra $(A,\circ)$ associated to an $A$-bimodule Novikov algebra which is a generalization of the definition of $\mathcal{O}$-operators and show that there are new Novikov algebra structures on the $A$-bimodule Novikov algebra obtained from extended $\mathcal{O}$-operators. We also introduce the definition of post-Novikov algebras and show that there is a close relationship between post-Novikov algebras and $\mathcal{O}$-operators of weight $λ$. The tensor form of extended $\mathcal{O}$-operators is also investigated which leads to the definition of extended Novikov Yang-Baxter equations, which is a generalization of the notion of Novikov Yang-Baxter equations. The relationships between extended $\mathcal{O}$-operators, Novikov Yang-Baxter equations, extended Novikov Yang-Baxter equations and generalized Novikov Yang-Baxter equations are established. |
| title | Extended $\mathcal{O}$-operators, Novikov Yang-Baxter equations and post-Novikov algebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2505.20735 |