Bialgebras, Manin triples of Malcev-Poisson algebras and post-Malcev-Poisson algebras
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910847601737728 |
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| author | Harrathi, Fattoum Mabrouk, Sami Nawel, Nasser Silvestrov, Sergei |
| author_facet | Harrathi, Fattoum Mabrouk, Sami Nawel, Nasser Silvestrov, Sergei |
| contents | A Malcev-Poisson algebra is a Malcev algebra together with a commutative associative algebra structure related by a Leibniz rule. In this paper, we introduce the notion of Malcev-Poisson bialgebra as an analogue of a Malcev bialgebra and establish the equivalence between matched pairs, Manin triples and Malcev-Poisson bialgebras. Moreover, we introduce a new algebraic structure, called post-Malcev-Poisson algebras. Post-Malcev-Poisson algebras can be viewed as the underlying algebraic structures of weighted relative Rota-Baxter operators on Malcev-Poisson algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_19709 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bialgebras, Manin triples of Malcev-Poisson algebras and post-Malcev-Poisson algebras Harrathi, Fattoum Mabrouk, Sami Nawel, Nasser Silvestrov, Sergei Rings and Algebras Quantum Algebra 17A30, 16D10, 17B63, 17D10, 17B38 A Malcev-Poisson algebra is a Malcev algebra together with a commutative associative algebra structure related by a Leibniz rule. In this paper, we introduce the notion of Malcev-Poisson bialgebra as an analogue of a Malcev bialgebra and establish the equivalence between matched pairs, Manin triples and Malcev-Poisson bialgebras. Moreover, we introduce a new algebraic structure, called post-Malcev-Poisson algebras. Post-Malcev-Poisson algebras can be viewed as the underlying algebraic structures of weighted relative Rota-Baxter operators on Malcev-Poisson algebras. |
| title | Bialgebras, Manin triples of Malcev-Poisson algebras and post-Malcev-Poisson algebras |
| topic | Rings and Algebras Quantum Algebra 17A30, 16D10, 17B63, 17D10, 17B38 |
| url | https://arxiv.org/abs/2502.19709 |