Nijenhuis operators and twisted $\mathcal{O}$-operators on Nambu-Poisson algebras
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911216685809664 |
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| author | Das, Apurba Harrathi, Fattoum Mabrouk, Sami |
| author_facet | Das, Apurba Harrathi, Fattoum Mabrouk, Sami |
| contents | A ternary Nambu-Poisson algebra (which we call a Nambu-Poisson algebra in the paper) is the underlying algebraic structure of Nambu-Poisson manifolds of order $3$ that appeared in the generalized Hamiltonian mechanics. First, we consider the 2nd cohomology group of a Nambu-Poisson algebra with coefficients in a given representation. Next, we discuss suitable linear deformations of a Nambu-Poisson algebra and show that any such trivial deformation yields a Nijenhuis operator on it. To understand the deformed Nambu-Poisson algebra obtained from a Nijenhuis operator, we introduce a new algebraic structure, which we name NS-Nambu-Poisson algebras. Finally, we consider $\mathcal{O}$-operators twisted by $2$-cocycles and find their close relationships with NS-Nambu-Poisson algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_15640 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nijenhuis operators and twisted $\mathcal{O}$-operators on Nambu-Poisson algebras Das, Apurba Harrathi, Fattoum Mabrouk, Sami Rings and Algebras Mathematical Physics Representation Theory 17B63, 17A40, 17B38, 17B40 A ternary Nambu-Poisson algebra (which we call a Nambu-Poisson algebra in the paper) is the underlying algebraic structure of Nambu-Poisson manifolds of order $3$ that appeared in the generalized Hamiltonian mechanics. First, we consider the 2nd cohomology group of a Nambu-Poisson algebra with coefficients in a given representation. Next, we discuss suitable linear deformations of a Nambu-Poisson algebra and show that any such trivial deformation yields a Nijenhuis operator on it. To understand the deformed Nambu-Poisson algebra obtained from a Nijenhuis operator, we introduce a new algebraic structure, which we name NS-Nambu-Poisson algebras. Finally, we consider $\mathcal{O}$-operators twisted by $2$-cocycles and find their close relationships with NS-Nambu-Poisson algebras. |
| title | Nijenhuis operators and twisted $\mathcal{O}$-operators on Nambu-Poisson algebras |
| topic | Rings and Algebras Mathematical Physics Representation Theory 17B63, 17A40, 17B38, 17B40 |
| url | https://arxiv.org/abs/2510.15640 |