Some generalizations of the variety of transposed Poisson algebras
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arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913232487186432 |
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| author | Sartayev, B. K. |
| author_facet | Sartayev, B. K. |
| contents | It is shown that the variety of transposed Poisson algebras coincides with the variety of Gelfand-Dorfman algebras in which the Novikov multiplication is commutative. The Gröbner-Shirshov basis for the transposed Poisson operad is calculated up to degree 4. Furthermore, we demonstrate that every transposed Poisson algebra is F-manifold. We verify that the special identities of GD-algebras hold in transposed Poisson algebras. Finally, we propose a conjecture stating that every transposed Poisson algebra is special, i.e., can be embedded into a differential Poisson algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_12869 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Some generalizations of the variety of transposed Poisson algebras Sartayev, B. K. Rings and Algebras It is shown that the variety of transposed Poisson algebras coincides with the variety of Gelfand-Dorfman algebras in which the Novikov multiplication is commutative. The Gröbner-Shirshov basis for the transposed Poisson operad is calculated up to degree 4. Furthermore, we demonstrate that every transposed Poisson algebra is F-manifold. We verify that the special identities of GD-algebras hold in transposed Poisson algebras. Finally, we propose a conjecture stating that every transposed Poisson algebra is special, i.e., can be embedded into a differential Poisson algebra. |
| title | Some generalizations of the variety of transposed Poisson algebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2305.12869 |