Double Poisson vertex algebras and non-commutative Hamiltonian equations
We develop the formalism of double Poisson vertex algebras (local and non-local) aimed at the study of non-commutative Hamiltonian PDEs. This is a generalization of the theory of double Poisson algebras, developed by Van den Bergh, which is used in the study of Hamiltonian ODEs. We apply our theory...
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| Format: | Article |
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Elsevier
2018
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| Online Access: | http://hdl.handle.net/1721.1/115829 https://orcid.org/0000-0002-2860-7811 |
| _version_ | 1826194149592793088 |
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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 develop the formalism of double Poisson vertex algebras (local and non-local) aimed at the study of non-commutative Hamiltonian PDEs. This is a generalization of the theory of double Poisson algebras, developed by Van den Bergh, which is used in the study of Hamiltonian ODEs. We apply our theory of double Poisson vertex algebras to non-commutative KP and Gelfand-Dickey hierarchies. We also construct the related non-commutative de Rham and variational complexes. Keywords: Double derivations; Double Poisson algebra; Double Poisson vertex algebra;
Integrable non-commutative Hamiltonian equation; Non-commutative de Rham and variational complexes; Non-commutative KP and Gelfand–Dickey equations |
| first_indexed | 2024-09-23T09:51:23Z |
| format | Article |
| id | mit-1721.1/115829 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T09:51:23Z |
| publishDate | 2018 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | mit-1721.1/1158292022-09-30T17:16:59Z Double Poisson vertex algebras and non-commutative Hamiltonian equations De Sole, Alberto Valeri, Daniele Kac, Victor Massachusetts Institute of Technology. Department of Mathematics Kac, Victor We develop the formalism of double Poisson vertex algebras (local and non-local) aimed at the study of non-commutative Hamiltonian PDEs. This is a generalization of the theory of double Poisson algebras, developed by Van den Bergh, which is used in the study of Hamiltonian ODEs. We apply our theory of double Poisson vertex algebras to non-commutative KP and Gelfand-Dickey hierarchies. We also construct the related non-commutative de Rham and variational complexes. Keywords: Double derivations; Double Poisson algebra; Double Poisson vertex algebra; Integrable non-commutative Hamiltonian equation; Non-commutative de Rham and variational complexes; Non-commutative KP and Gelfand–Dickey equations 2018-05-23T18:42:44Z 2018-05-23T18:42:44Z 2015-06 2015-05 2018-05-23T18:03:11Z Article http://purl.org/eprint/type/JournalArticle 0001-8708 1090-2082 http://hdl.handle.net/1721.1/115829 De Sole, Alberto et al. “Double Poisson Vertex Algebras and Non-Commutative Hamiltonian Equations.” Advances in Mathematics 281 (August 2015): 1025–1099 © 2015 Elsevier Inc https://orcid.org/0000-0002-2860-7811 http://dx.doi.org/10.1016/J.AIM.2015.05.011 Advances in Mathematics Creative Commons Attribution-NonCommercial-NoDerivs License http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier arXiv |
| spellingShingle | De Sole, Alberto Valeri, Daniele Kac, Victor Double Poisson vertex algebras and non-commutative Hamiltonian equations |
| title | Double Poisson vertex algebras and non-commutative Hamiltonian equations |
| title_full | Double Poisson vertex algebras and non-commutative Hamiltonian equations |
| title_fullStr | Double Poisson vertex algebras and non-commutative Hamiltonian equations |
| title_full_unstemmed | Double Poisson vertex algebras and non-commutative Hamiltonian equations |
| title_short | Double Poisson vertex algebras and non-commutative Hamiltonian equations |
| title_sort | double poisson vertex algebras and non commutative hamiltonian equations |
| url | http://hdl.handle.net/1721.1/115829 https://orcid.org/0000-0002-2860-7811 |
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