Computation of cohomology of vertex algebras
© 2020, The Mathematical Society of Japan and Springer Japan KK, part of Springer Nature. We review cohomology theories corresponding to the chiral and classical operads. The first one is the cohomology theory of vertex algebras, while the second one is the classical cohomology of Poisson vertex alg...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Springer Science and Business Media LLC
2021
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| Online Access: | https://hdl.handle.net/1721.1/136076 |
| _version_ | 1826212312525045760 |
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| author | Bakalov, Bojko De Sole, Alberto Kac, Victor G |
| author_facet | Bakalov, Bojko De Sole, Alberto Kac, Victor G |
| author_sort | Bakalov, Bojko |
| collection | MIT |
| description | © 2020, The Mathematical Society of Japan and Springer Japan KK, part of Springer Nature. We review cohomology theories corresponding to the chiral and classical operads. The first one is the cohomology theory of vertex algebras, while the second one is the classical cohomology of Poisson vertex algebras (PVA), and we construct a spectral sequence relating them. Since in “good” cases the classical PVA cohomology coincides with the variational PVA cohomology and there are well-developed methods to compute the latter, this enables us to compute the cohomology of vertex algebras in many interesting cases. Finally, we describe a unified approach to integrability through vanishing of the first cohomology, which is applicable to both classical and quantum systems of Hamiltonian PDEs. |
| first_indexed | 2024-09-23T15:19:44Z |
| format | Article |
| id | mit-1721.1/136076 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T15:19:44Z |
| publishDate | 2021 |
| publisher | Springer Science and Business Media LLC |
| record_format | dspace |
| spelling | mit-1721.1/1360762021-11-27T03:54:28Z Computation of cohomology of vertex algebras Bakalov, Bojko De Sole, Alberto Kac, Victor G © 2020, The Mathematical Society of Japan and Springer Japan KK, part of Springer Nature. We review cohomology theories corresponding to the chiral and classical operads. The first one is the cohomology theory of vertex algebras, while the second one is the classical cohomology of Poisson vertex algebras (PVA), and we construct a spectral sequence relating them. Since in “good” cases the classical PVA cohomology coincides with the variational PVA cohomology and there are well-developed methods to compute the latter, this enables us to compute the cohomology of vertex algebras in many interesting cases. Finally, we describe a unified approach to integrability through vanishing of the first cohomology, which is applicable to both classical and quantum systems of Hamiltonian PDEs. 2021-10-27T20:30:42Z 2021-10-27T20:30:42Z 2021 2021-05-21T17:06:47Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/136076 en 10.1007/s11537-020-2034-9 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 | Bakalov, Bojko De Sole, Alberto Kac, Victor G Computation of cohomology of vertex algebras |
| title | Computation of cohomology of vertex algebras |
| title_full | Computation of cohomology of vertex algebras |
| title_fullStr | Computation of cohomology of vertex algebras |
| title_full_unstemmed | Computation of cohomology of vertex algebras |
| title_short | Computation of cohomology of vertex algebras |
| title_sort | computation of cohomology of vertex algebras |
| url | https://hdl.handle.net/1721.1/136076 |
| work_keys_str_mv | AT bakalovbojko computationofcohomologyofvertexalgebras AT desolealberto computationofcohomologyofvertexalgebras AT kacvictorg computationofcohomologyofvertexalgebras |