Functorial constructions related to double Poisson vertex algebras
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911174003523584 |
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| author | Bozec, Tristan Fairon, Maxime Moreau, Anne |
| author_facet | Bozec, Tristan Fairon, Maxime Moreau, Anne |
| contents | For any double Poisson algebra, we produce a double Poisson vertex algebra using the jet algebra construction. We show that this construction is compatible with the representation functor which associates to any double Poisson (vertex) algebra and any positive integer a Poisson (vertex) algebra. We also consider related constructions, such as Poisson reductions and Hamiltonian reductions, with the aim of comparing the different corresponding categories. This allows us to provide various interesting examples of double Poisson vertex algebras, in particular from double quivers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_06071 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Functorial constructions related to double Poisson vertex algebras Bozec, Tristan Fairon, Maxime Moreau, Anne Representation Theory Algebraic Geometry Rings and Algebras Symplectic Geometry 17B63, 17B69, 14L30, 16S38 For any double Poisson algebra, we produce a double Poisson vertex algebra using the jet algebra construction. We show that this construction is compatible with the representation functor which associates to any double Poisson (vertex) algebra and any positive integer a Poisson (vertex) algebra. We also consider related constructions, such as Poisson reductions and Hamiltonian reductions, with the aim of comparing the different corresponding categories. This allows us to provide various interesting examples of double Poisson vertex algebras, in particular from double quivers. |
| title | Functorial constructions related to double Poisson vertex algebras |
| topic | Representation Theory Algebraic Geometry Rings and Algebras Symplectic Geometry 17B63, 17B69, 14L30, 16S38 |
| url | https://arxiv.org/abs/2307.06071 |