An operadic approach to vertex algebra and Poisson vertex algebra cohomology
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 the vertex algebra cohomology complex. Likewise, the associated grad...
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| Format: | Article |
| Language: | English |
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Springer Science and Business Media LLC
2020
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| Online Access: | https://hdl.handle.net/1721.1/124818 |
| _version_ | 1826214544026894336 |
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| author | Kac, Victor |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Kac, Victor |
| author_sort | Kac, Victor |
| collection | MIT |
| description | 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 the vertex algebra cohomology complex. Likewise, the associated graded of the chiral operad leads to the 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. ©2019 |
| first_indexed | 2024-09-23T16:07:27Z |
| format | Article |
| id | mit-1721.1/124818 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T16:07:27Z |
| publishDate | 2020 |
| publisher | Springer Science and Business Media LLC |
| record_format | dspace |
| spelling | mit-1721.1/1248182022-09-29T18:22:45Z An operadic approach to vertex algebra and Poisson vertex algebra cohomology An operadic approach to vertex algebra and Poisson vertex algebra cohomology Kac, Victor Massachusetts Institute of Technology. Department of Mathematics 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 the vertex algebra cohomology complex. Likewise, the associated graded of the chiral operad leads to the 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. ©2019 2020-04-22T19:48:18Z 2020-04-22T19:48:18Z 2019-06 2019-11-14T16:58:38Z Article http://purl.org/eprint/type/JournalArticle 1861-3624 https://hdl.handle.net/1721.1/124818 Bakalov, Bojko, Alberto De Sole, Reimundo Heluani , and Victor G. Kac, "An operadic approach to vertex algebra and Poisson vertex algebra cohomology." Japanese journal of mathematics 14 (June 2019): p. 249-342 doi 10.1007/S11537-019-1825-3 ©2019 Author(s) en 10.1007/S11537-019-1825-3 Japanese journal of mathematics Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Springer Science and Business Media LLC arXiv |
| spellingShingle | Kac, Victor An operadic approach to vertex algebra and Poisson vertex algebra cohomology |
| title | An operadic approach to vertex algebra and Poisson vertex algebra cohomology |
| title_full | An operadic approach to vertex algebra and Poisson vertex algebra cohomology |
| title_fullStr | An operadic approach to vertex algebra and Poisson vertex algebra cohomology |
| title_full_unstemmed | An operadic approach to vertex algebra and Poisson vertex algebra cohomology |
| title_short | An operadic approach to vertex algebra and Poisson vertex algebra cohomology |
| title_sort | operadic approach to vertex algebra and poisson vertex algebra cohomology |
| url | https://hdl.handle.net/1721.1/124818 |
| work_keys_str_mv | AT kacvictor anoperadicapproachtovertexalgebraandpoissonvertexalgebracohomology AT kacvictor operadicapproachtovertexalgebraandpoissonvertexalgebracohomology |