Universal enveloping algebras of weighted differential Poisson algebras
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866916468620263424 |
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| author | Chen, Ying Kang, Chuangchuang Lü, Jiafeng |
| author_facet | Chen, Ying Kang, Chuangchuang Lü, Jiafeng |
| contents | The $λ$-differential operators and modified $λ$-differential operators are generalizations of classical differential operators. This paper introduces the notions of $λ$-differential Poisson ($λ$-DP for short) algebras and modified $λ$-differential Poisson ($λ$-mDP for short) algebras as generalizations of differential Poisson algebras. The $λ$-DP algebra is proved to be closed under tensor product, and a $λ$-DP algebra structure is provided on the cohomology algebra of the $λ$-DP algebra. These conclusions are also applied to $λ$-mDP algebras and their modules. Finally, the universal enveloping algebras of $λ$-DP algebras are generalized by constructing a $\mathcal{P}$-triple. Three isomorphisms among opposite algebras, tensor algebras and the universal enveloping algebras of $λ$-DP algebras are obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03046 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universal enveloping algebras of weighted differential Poisson algebras Chen, Ying Kang, Chuangchuang Lü, Jiafeng Mathematical Physics 16S10, 16S30, 17B35, 17B63, The $λ$-differential operators and modified $λ$-differential operators are generalizations of classical differential operators. This paper introduces the notions of $λ$-differential Poisson ($λ$-DP for short) algebras and modified $λ$-differential Poisson ($λ$-mDP for short) algebras as generalizations of differential Poisson algebras. The $λ$-DP algebra is proved to be closed under tensor product, and a $λ$-DP algebra structure is provided on the cohomology algebra of the $λ$-DP algebra. These conclusions are also applied to $λ$-mDP algebras and their modules. Finally, the universal enveloping algebras of $λ$-DP algebras are generalized by constructing a $\mathcal{P}$-triple. Three isomorphisms among opposite algebras, tensor algebras and the universal enveloping algebras of $λ$-DP algebras are obtained. |
| title | Universal enveloping algebras of weighted differential Poisson algebras |
| topic | Mathematical Physics 16S10, 16S30, 17B35, 17B63, |
| url | https://arxiv.org/abs/2411.03046 |