On Poisson superalgebras in characteristic 2
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917131588730880 |
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| author | Ehret, Quentin |
| author_facet | Ehret, Quentin |
| contents | This paper is devoted to the study of Poisson superalgebras over fields of characteristic $2$. We investigate their representations, semidirect products, cohomology, formal deformations, and universal enveloping algebras. We also introduce Lie-Rinehart superalgebras in characteristic $2$ and clarify their connections with Poisson superalgebras. In particular, we show that the universal enveloping algebra of a Poisson superalgebra coincides with the universal enveloping algebra of an associated Lie-Rinehart superalgebra. We also compute examples and initiate the study of pre-Poisson superalgebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06680 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Poisson superalgebras in characteristic 2 Ehret, Quentin Representation Theory Rings and Algebras 17B50, 17B63, 17B60, 17B35 This paper is devoted to the study of Poisson superalgebras over fields of characteristic $2$. We investigate their representations, semidirect products, cohomology, formal deformations, and universal enveloping algebras. We also introduce Lie-Rinehart superalgebras in characteristic $2$ and clarify their connections with Poisson superalgebras. In particular, we show that the universal enveloping algebra of a Poisson superalgebra coincides with the universal enveloping algebra of an associated Lie-Rinehart superalgebra. We also compute examples and initiate the study of pre-Poisson superalgebras. |
| title | On Poisson superalgebras in characteristic 2 |
| topic | Representation Theory Rings and Algebras 17B50, 17B63, 17B60, 17B35 |
| url | https://arxiv.org/abs/2512.06680 |