An operadic approach to vertex algebra and Poisson vertex algebra cohomology
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2018
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| _version_ | 1866914626593095680 |
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| author | Bakalov, Bojko De Sole, Alberto Heluani, Reimundo Kac, Victor G. |
| author_facet | Bakalov, Bojko De Sole, Alberto Heluani, Reimundo Kac, Victor G. |
| contents | We translate the construction of the chiral operad by Beilinson and Drinfeld to the purely algebraic language of vertex algebras. Consequently, the general construction of a cohomology complex associated to a linear operad produces a vertex algebra cohomology complex. Likewise, the associated graded of the chiral operad leads to a classical operad, which produces a Poisson vertex algebra cohomology complex. The latter is closely related to the variational Poisson cohomology studied by two of the authors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1806_08754 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | An operadic approach to vertex algebra and Poisson vertex algebra cohomology Bakalov, Bojko De Sole, Alberto Heluani, Reimundo Kac, Victor G. Representation Theory Mathematical Physics 17B69 (Primary), 18D50, 17B65, 17B63, 17B80 (Secondary) We translate the construction of the chiral operad by Beilinson and Drinfeld to the purely algebraic language of vertex algebras. Consequently, the general construction of a cohomology complex associated to a linear operad produces a vertex algebra cohomology complex. Likewise, the associated graded of the chiral operad leads to a classical operad, which produces a Poisson vertex algebra cohomology complex. The latter is closely related to the variational Poisson cohomology studied by two of the authors. |
| title | An operadic approach to vertex algebra and Poisson vertex algebra cohomology |
| topic | Representation Theory Mathematical Physics 17B69 (Primary), 18D50, 17B65, 17B63, 17B80 (Secondary) |
| url | https://arxiv.org/abs/1806.08754 |