On Poisson conformal bialgebras
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910588347613184 |
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| author | Hong, Yanyong Bai, Chengming |
| author_facet | Hong, Yanyong Bai, Chengming |
| contents | We develop a conformal analog of the theory of Poisson bialgebras as well as a bialgebra theory of Poisson conformal algebras. We introduce the notion of Poisson conformal bialgebras, which are characterized by Manin triples of Poisson conformal algebras. A class of special Poisson conformal bialgebras called coboundary Poisson conformal bialgebras are constructed from skew-symmetric solutions of the Poisson conformal Yang-Baxter equation, whose operator forms are studied. Then we show that the semi-classical limits of conformal formal deformations of commutative and cocommutative antisymmetric infinitesimal conformal bialgebras are Poisson conformal bialgebras. Finally, we extend the correspondence between Poisson conformal algebras and Poisson-Gel'fand-Dorfman algebras to the context of bialgebras, that is, we introduce the notion of Poisson-Gel'fand-Dorfman bialgebras and show that Poisson-Gel'fand-Dorfman bialgebras correspond to a class of Poisson conformal bialgebras. Moreover, a construction of Poisson conformal bialgebras from pre-Poisson-Gel'fand-Dorfman algebras is given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01619 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Poisson conformal bialgebras Hong, Yanyong Bai, Chengming Rings and Algebras Representation Theory We develop a conformal analog of the theory of Poisson bialgebras as well as a bialgebra theory of Poisson conformal algebras. We introduce the notion of Poisson conformal bialgebras, which are characterized by Manin triples of Poisson conformal algebras. A class of special Poisson conformal bialgebras called coboundary Poisson conformal bialgebras are constructed from skew-symmetric solutions of the Poisson conformal Yang-Baxter equation, whose operator forms are studied. Then we show that the semi-classical limits of conformal formal deformations of commutative and cocommutative antisymmetric infinitesimal conformal bialgebras are Poisson conformal bialgebras. Finally, we extend the correspondence between Poisson conformal algebras and Poisson-Gel'fand-Dorfman algebras to the context of bialgebras, that is, we introduce the notion of Poisson-Gel'fand-Dorfman bialgebras and show that Poisson-Gel'fand-Dorfman bialgebras correspond to a class of Poisson conformal bialgebras. Moreover, a construction of Poisson conformal bialgebras from pre-Poisson-Gel'fand-Dorfman algebras is given. |
| title | On Poisson conformal bialgebras |
| topic | Rings and Algebras Representation Theory |
| url | https://arxiv.org/abs/2409.01619 |