Algebraic proofs for shallow water bi–Hamiltonian systems for three cocycle of the semi-direct product of Kac–Moody and Virasoro Lie algebras
We prove new theorems related to the construction of the shallow water bi-Hamiltonian systems associated to the semi-direct product of Virasoro and affine Kac–Moody Lie algebras. We discuss associated Verma modules, coadjoint orbits, Casimir functions, and bi-Hamiltonian systems.
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| Format: | Article |
| Language: | English |
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De Gruyter
2018-01-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2018-0002 |
| _version_ | 1818733602411642880 |
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| author | Zuevsky A. |
| author_facet | Zuevsky A. |
| author_sort | Zuevsky A. |
| collection | DOAJ |
| description | We prove new theorems related to the construction of the shallow water bi-Hamiltonian systems associated to the semi-direct product of Virasoro and affine Kac–Moody Lie algebras. We discuss associated Verma modules, coadjoint orbits, Casimir functions, and bi-Hamiltonian systems. |
| first_indexed | 2024-12-17T23:52:04Z |
| format | Article |
| id | doaj.art-7baf9e1610df4913a13c1f92b0d3c682 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-17T23:52:04Z |
| publishDate | 2018-01-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-7baf9e1610df4913a13c1f92b0d3c6822022-12-21T21:28:10ZengDe GruyterOpen Mathematics2391-54552018-01-011611810.1515/math-2018-0002math-2018-0002Algebraic proofs for shallow water bi–Hamiltonian systems for three cocycle of the semi-direct product of Kac–Moody and Virasoro Lie algebrasZuevsky A.0Institute of Mathemtics, Czech Academy of Sciences, Prague, Czech RepublicWe prove new theorems related to the construction of the shallow water bi-Hamiltonian systems associated to the semi-direct product of Virasoro and affine Kac–Moody Lie algebras. We discuss associated Verma modules, coadjoint orbits, Casimir functions, and bi-Hamiltonian systems.https://doi.org/10.1515/math-2018-0002affine kac–moody lie algebrasbi-hamiltonian systemsverma modulescoadjoint orbits17b6917b0870g6082c23 |
| spellingShingle | Zuevsky A. Algebraic proofs for shallow water bi–Hamiltonian systems for three cocycle of the semi-direct product of Kac–Moody and Virasoro Lie algebras Open Mathematics affine kac–moody lie algebras bi-hamiltonian systems verma modules coadjoint orbits 17b69 17b08 70g60 82c23 |
| title | Algebraic proofs for shallow water bi–Hamiltonian systems for three cocycle of the semi-direct product of Kac–Moody and Virasoro Lie algebras |
| title_full | Algebraic proofs for shallow water bi–Hamiltonian systems for three cocycle of the semi-direct product of Kac–Moody and Virasoro Lie algebras |
| title_fullStr | Algebraic proofs for shallow water bi–Hamiltonian systems for three cocycle of the semi-direct product of Kac–Moody and Virasoro Lie algebras |
| title_full_unstemmed | Algebraic proofs for shallow water bi–Hamiltonian systems for three cocycle of the semi-direct product of Kac–Moody and Virasoro Lie algebras |
| title_short | Algebraic proofs for shallow water bi–Hamiltonian systems for three cocycle of the semi-direct product of Kac–Moody and Virasoro Lie algebras |
| title_sort | algebraic proofs for shallow water bi hamiltonian systems for three cocycle of the semi direct product of kac moody and virasoro lie algebras |
| topic | affine kac–moody lie algebras bi-hamiltonian systems verma modules coadjoint orbits 17b69 17b08 70g60 82c23 |
| url | https://doi.org/10.1515/math-2018-0002 |
| work_keys_str_mv | AT zuevskya algebraicproofsforshallowwaterbihamiltoniansystemsforthreecocycleofthesemidirectproductofkacmoodyandvirasoroliealgebras |