Salvato in:
| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2505.08494 |
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Sommario:
- The notions of Poisson $H$-pseudoalgebras are generalizations of Poisson algebras in a pseudotensor category $\mathcal{M}^{\ast}(H)$. This paper introduces an analogue of Poisson-Ore extension in Poisson $H$-pseudoalgebras. Poisson $H$-pseudoalgebras with the differential graded setting induces the notions of differential graded Poisson $H$-pseudoalgebras (DGP pseudoalgebras, for short). The DGP pseudoalgebra with some compatibility conditions is proved to be closed under tensor product. Furthermore, the universal enveloping $H$-pseudoalgebras of DGP pseudoalgebras are constructed by a $\mathcal{P}$-triple. A unique differential graded pseudoalgebra homomorphism between a universal enveloping $H$-pseudoalgebra of a DGP pseudoalgebra and a $\mathcal{P}$-triple of a DGP pseudoalgebra is obtained.