Matched pairs and double construction bialgebras of (transposed) Poisson 3-Lie algebras
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915343904014336 |
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| author | Zhou, Kecheng Kang, Chuangchuang Lü, Jiafeng |
| author_facet | Zhou, Kecheng Kang, Chuangchuang Lü, Jiafeng |
| contents | Double construction bialgebras for Poisson 3-Lie algebras and transposed Poisson 3-Lie algebras are defined and studied using matched pairs. Poisson 3-Lie algebras and transposed Poisson 3-Lie algebras are constructed on direct sums and tensor products of vector spaces. Matched pairs, Manin triples, and double construction Poisson 3-Lie bialgebras are shown to be equivalent. Since the double construction approach does not apply to bialgebra theory for transposed Poisson 3-Lie algebras, admissible transposed Poisson 3-Lie algebras are introduced. These algebras are both transposed Poisson 3-Lie algebras and Poisson 3-Lie algebras. An equivalence between matched pairs and double construction admissible transposed Poisson 3-Lie bialgebras is established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_12690 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Matched pairs and double construction bialgebras of (transposed) Poisson 3-Lie algebras Zhou, Kecheng Kang, Chuangchuang Lü, Jiafeng Rings and Algebras 17A40, 16T10, 17A30, 17A42, 17B10, 17B63 Double construction bialgebras for Poisson 3-Lie algebras and transposed Poisson 3-Lie algebras are defined and studied using matched pairs. Poisson 3-Lie algebras and transposed Poisson 3-Lie algebras are constructed on direct sums and tensor products of vector spaces. Matched pairs, Manin triples, and double construction Poisson 3-Lie bialgebras are shown to be equivalent. Since the double construction approach does not apply to bialgebra theory for transposed Poisson 3-Lie algebras, admissible transposed Poisson 3-Lie algebras are introduced. These algebras are both transposed Poisson 3-Lie algebras and Poisson 3-Lie algebras. An equivalence between matched pairs and double construction admissible transposed Poisson 3-Lie bialgebras is established. |
| title | Matched pairs and double construction bialgebras of (transposed) Poisson 3-Lie algebras |
| topic | Rings and Algebras 17A40, 16T10, 17A30, 17A42, 17B10, 17B63 |
| url | https://arxiv.org/abs/2506.12690 |