Classical W-Algebras and Generalized Drinfeld-Sokolov Bi-Hamiltonian Systems Within the Theory of Poisson Vertex Algebras
We describe of the generalized Drinfeld-Sokolov Hamiltonian reduction for the construction of classical W-algebras within the framework of Poisson vertex algebras. In this context, the gauge group action on the phase space is translated in terms of (the exponential of) a Lie conformal algebra action...
| Main Authors: | , , |
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| Format: | Article |
| Language: | en_US |
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Springer-Verlag
2015
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| Online Access: | http://hdl.handle.net/1721.1/92904 https://orcid.org/0000-0002-2860-7811 |
| _version_ | 1826208364565102592 |
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| author | De Sole, Alberto Valeri, Daniele Kac, Victor |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics De Sole, Alberto Valeri, Daniele Kac, Victor |
| author_sort | De Sole, Alberto |
| collection | MIT |
| description | We describe of the generalized Drinfeld-Sokolov Hamiltonian reduction for the construction of classical W-algebras within the framework of Poisson vertex algebras. In this context, the gauge group action on the phase space is translated in terms of (the exponential of) a Lie conformal algebra action on the space of functions. Following the ideas of Drinfeld and Sokolov, we then establish under certain sufficient conditions the applicability of the Lenard-Magri scheme of integrability and the existence of the corresponding integrable hierarchy of bi-Hamiltonian equations. |
| first_indexed | 2024-09-23T14:04:37Z |
| format | Article |
| id | mit-1721.1/92904 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:04:37Z |
| publishDate | 2015 |
| publisher | Springer-Verlag |
| record_format | dspace |
| spelling | mit-1721.1/929042022-09-28T18:12:58Z Classical W-Algebras and Generalized Drinfeld-Sokolov Bi-Hamiltonian Systems Within the Theory of Poisson Vertex Algebras De Sole, Alberto Valeri, Daniele Kac, Victor Massachusetts Institute of Technology. Department of Mathematics Kac, Victor We describe of the generalized Drinfeld-Sokolov Hamiltonian reduction for the construction of classical W-algebras within the framework of Poisson vertex algebras. In this context, the gauge group action on the phase space is translated in terms of (the exponential of) a Lie conformal algebra action on the space of functions. Following the ideas of Drinfeld and Sokolov, we then establish under certain sufficient conditions the applicability of the Lenard-Magri scheme of integrability and the existence of the corresponding integrable hierarchy of bi-Hamiltonian equations. 2015-01-15T19:32:20Z 2015-01-15T19:32:20Z 2013-08 Article http://purl.org/eprint/type/JournalArticle 0010-3616 1432-0916 http://hdl.handle.net/1721.1/92904 De Sole, Alberto, Victor G. Kac, and Daniele Valeri. “Classical W-Algebras and Generalized Drinfeld-Sokolov Bi-Hamiltonian Systems Within the Theory of Poisson Vertex Algebras.” Commun. Math. Phys. 323, no. 2 (August 22, 2013): 663–711. https://orcid.org/0000-0002-2860-7811 en_US http://dx.doi.org/10.1007/s00220-013-1785-z Communications in Mathematical Physics Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Springer-Verlag arXiv |
| spellingShingle | De Sole, Alberto Valeri, Daniele Kac, Victor Classical W-Algebras and Generalized Drinfeld-Sokolov Bi-Hamiltonian Systems Within the Theory of Poisson Vertex Algebras |
| title | Classical W-Algebras and Generalized Drinfeld-Sokolov Bi-Hamiltonian Systems Within the Theory of Poisson Vertex Algebras |
| title_full | Classical W-Algebras and Generalized Drinfeld-Sokolov Bi-Hamiltonian Systems Within the Theory of Poisson Vertex Algebras |
| title_fullStr | Classical W-Algebras and Generalized Drinfeld-Sokolov Bi-Hamiltonian Systems Within the Theory of Poisson Vertex Algebras |
| title_full_unstemmed | Classical W-Algebras and Generalized Drinfeld-Sokolov Bi-Hamiltonian Systems Within the Theory of Poisson Vertex Algebras |
| title_short | Classical W-Algebras and Generalized Drinfeld-Sokolov Bi-Hamiltonian Systems Within the Theory of Poisson Vertex Algebras |
| title_sort | classical w algebras and generalized drinfeld sokolov bi hamiltonian systems within the theory of poisson vertex algebras |
| url | http://hdl.handle.net/1721.1/92904 https://orcid.org/0000-0002-2860-7811 |
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