On the Lie algebra structures connected with Hamiltonian dynamical systems
We construct the hierarchies of master symmetries constituting Virasoro-type algebras for the Hamiltonian vector fields preserving a recursion operator. Similarly, repeatedly contracting a Hamiltonian vector field with the corresponding recursion operator, we define an Abelian Lie algebra of the thu...
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| Date: | 1997 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1997
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5051 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511245553106944 |
|---|---|
| author | Smirnov, R. G. Смирнов, Р. Г. |
| author_facet | Smirnov, R. G. Смирнов, Р. Г. |
| author_sort | Smirnov, R. G. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:23:40Z |
| description | We construct the hierarchies of master symmetries constituting Virasoro-type algebras for the Hamiltonian vector fields preserving a recursion operator. Similarly, repeatedly contracting a Hamiltonian vector field with the corresponding recursion operator, we define an Abelian Lie algebra of the thus obtained hierarchy of vector fields. The approach is shown to be applicable for the Volterra and Toda lattices. |
| first_indexed | 2026-03-24T03:09:50Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5051 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:09:50Z |
| publishDate | 1997 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/b4/dc5ed5a6786274d7b9888bf4e32082b4.pdf |
| spelling | umjimathkievua-article-50512020-03-18T21:23:40Z On the Lie algebra structures connected with Hamiltonian dynamical systems Про структури алгебр Лі, пов'язаних з гамільтоновими динамічними системами Smirnov, R. G. Смирнов, Р. Г. We construct the hierarchies of master symmetries constituting Virasoro-type algebras for the Hamiltonian vector fields preserving a recursion operator. Similarly, repeatedly contracting a Hamiltonian vector field with the corresponding recursion operator, we define an Abelian Lie algebra of the thus obtained hierarchy of vector fields. The approach is shown to be applicable for the Volterra and Toda lattices. Для гамільтоиових систем з рекурсивним оператором ієрархії будується мастер симетрій, які формують алгебри Лі типу Вірасоро. Аналогічно, повторно діючи рекурсивним оператором на гамільтонів потік, одержується ієрархія векторних полів, що складають абелеву алгберу Лі. Цей підхід застосовано до систем Вольтерра і Тода. Institute of Mathematics, NAS of Ukraine 1997-05-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5051 Ukrains’kyi Matematychnyi Zhurnal; Vol. 49 No. 5 (1997); 699–705 Український математичний журнал; Том 49 № 5 (1997); 699–705 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/5051/6799 https://umj.imath.kiev.ua/index.php/umj/article/view/5051/6800 Copyright (c) 1997 Smirnov R. G. |
| spellingShingle | Smirnov, R. G. Смирнов, Р. Г. On the Lie algebra structures connected with Hamiltonian dynamical systems |
| title | On the Lie algebra structures connected with Hamiltonian dynamical systems |
| title_alt | Про структури алгебр Лі, пов'язаних з гамільтоновими динамічними системами |
| title_full | On the Lie algebra structures connected with Hamiltonian dynamical systems |
| title_fullStr | On the Lie algebra structures connected with Hamiltonian dynamical systems |
| title_full_unstemmed | On the Lie algebra structures connected with Hamiltonian dynamical systems |
| title_short | On the Lie algebra structures connected with Hamiltonian dynamical systems |
| title_sort | on the lie algebra structures connected with hamiltonian dynamical systems |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5051 |
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