On transposed Poisson conformal superalgebras
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918508236898304 |
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| author | Fang, Hao Yuan, Lamei |
| author_facet | Fang, Hao Yuan, Lamei |
| contents | We introduce and study transposed Poisson conformal superalgebras, the $\mathbb Z_2$-graded conformal analogues of transposed Poisson algebras, as well as their noncommutative variants. We derive a family of identities forced by the transposed conformal super-Leibniz rule and prove that the tensor product over $\mathbb C[\partial]$ of two such superalgebras again carries a natural transposed Poisson conformal superalgebra structure. Moreover, we display a close relationship between transposed Poisson conformal superalgebras and Hom-Lie conformal superalgebras, and give the compatibility conditions between a Poisson conformal superalgebra and a transposed Poisson conformal superalgebra. In addition, several constructions are obtained from modified Lie conformal brackets and from Novikov-Poisson, pre-Lie commutative, differential Novikov-Poisson, and pre-Lie Poisson conformal superalgebras. Finally, using the known classification of Lie conformal superalgebras of rank (1+1), we determine all compatible transposed Poisson conformal superalgebra structures on such superalgebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_17747 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On transposed Poisson conformal superalgebras Fang, Hao Yuan, Lamei Rings and Algebras Mathematical Physics 17B60, 17B61, 17B63, 17B69, 17B70 We introduce and study transposed Poisson conformal superalgebras, the $\mathbb Z_2$-graded conformal analogues of transposed Poisson algebras, as well as their noncommutative variants. We derive a family of identities forced by the transposed conformal super-Leibniz rule and prove that the tensor product over $\mathbb C[\partial]$ of two such superalgebras again carries a natural transposed Poisson conformal superalgebra structure. Moreover, we display a close relationship between transposed Poisson conformal superalgebras and Hom-Lie conformal superalgebras, and give the compatibility conditions between a Poisson conformal superalgebra and a transposed Poisson conformal superalgebra. In addition, several constructions are obtained from modified Lie conformal brackets and from Novikov-Poisson, pre-Lie commutative, differential Novikov-Poisson, and pre-Lie Poisson conformal superalgebras. Finally, using the known classification of Lie conformal superalgebras of rank (1+1), we determine all compatible transposed Poisson conformal superalgebra structures on such superalgebras. |
| title | On transposed Poisson conformal superalgebras |
| topic | Rings and Algebras Mathematical Physics 17B60, 17B61, 17B63, 17B69, 17B70 |
| url | https://arxiv.org/abs/2605.17747 |