Affine and Finite Lie Algebras and Integrable Toda Field Equations on Discrete Space-Time
Difference-difference systems are suggested corresponding to the Cartan matrices of any simple or affine Lie algebra. In the cases of the algebras AN, BN, CN, G₂, D₃, A₁⁽¹⁾, A₂⁽²⁾, DN⁽²⁾ these systems are proved to be integrable. For the systems corresponding to the algebras A₂, A₁⁽¹⁾, A₂⁽²⁾ genera...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2012 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2012
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/148464 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Affine and Finite Lie Algebras and Integrable Toda Field Equations on Discrete Space-Time / R. Garifullin, I. Habibullin, M. Yangubaeva // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 41 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862580832827342848 |
|---|---|
| author | Garifullin, R. Habibullin, I. Yangubaeva, M. |
| author_facet | Garifullin, R. Habibullin, I. Yangubaeva, M. |
| citation_txt | Affine and Finite Lie Algebras and Integrable Toda Field Equations on Discrete Space-Time / R. Garifullin, I. Habibullin, M. Yangubaeva // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 41 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Difference-difference systems are suggested corresponding to the Cartan matrices of any simple or affine Lie algebra. In the cases of the algebras AN, BN, CN, G₂, D₃, A₁⁽¹⁾, A₂⁽²⁾, DN⁽²⁾ these systems are proved to be integrable. For the systems corresponding to the algebras A₂, A₁⁽¹⁾, A₂⁽²⁾ generalized symmetries are found. For the systems A₂, B₂, C₂, G₂, D₃ complete sets of independent integrals are found. The Lax representation for the difference-difference systems corresponding to AN, BN, CN, A₁⁽¹⁾,DN⁽²⁾ are presented.
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| first_indexed | 2025-11-26T20:27:20Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148464 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-26T20:27:20Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Garifullin, R. Habibullin, I. Yangubaeva, M. 2019-02-18T13:17:26Z 2019-02-18T13:17:26Z 2012 Affine and Finite Lie Algebras and Integrable Toda Field Equations on Discrete Space-Time / R. Garifullin, I. Habibullin, M. Yangubaeva // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 41 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 35Q53; 37K40 DOI: http://dx.doi.org/10.3842/SIGMA.2012.062 https://nasplib.isofts.kiev.ua/handle/123456789/148464 Difference-difference systems are suggested corresponding to the Cartan matrices of any simple or affine Lie algebra. In the cases of the algebras AN, BN, CN, G₂, D₃, A₁⁽¹⁾, A₂⁽²⁾, DN⁽²⁾ these systems are proved to be integrable. For the systems corresponding to the algebras A₂, A₁⁽¹⁾, A₂⁽²⁾ generalized symmetries are found. For the systems A₂, B₂, C₂, G₂, D₃ complete sets of independent integrals are found. The Lax representation for the difference-difference systems corresponding to AN, BN, CN, A₁⁽¹⁾,DN⁽²⁾ are presented. This paper is a contribution to the Special Issue “Geometrical Methods in Mathematical Physics”. The full collection is available at http://www.emis.de/journals/SIGMA/GMMP2012.html.
 The authors are grateful to the referees for their important contribution to improve the article. This work is partially supported by Russian Foundation for Basic Research (RFBR) grants 11-01-97005-r-povoljie-a, 12-01-31208-mol a and 10-01-00088-a and by Federal Task Program “Scientific and pedagogical staf f of innovative Russia for 2009–2013” contract no. 2012-1.5-12-000-1003-011. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Affine and Finite Lie Algebras and Integrable Toda Field Equations on Discrete Space-Time Article published earlier |
| spellingShingle | Affine and Finite Lie Algebras and Integrable Toda Field Equations on Discrete Space-Time Garifullin, R. Habibullin, I. Yangubaeva, M. |
| title | Affine and Finite Lie Algebras and Integrable Toda Field Equations on Discrete Space-Time |
| title_full | Affine and Finite Lie Algebras and Integrable Toda Field Equations on Discrete Space-Time |
| title_fullStr | Affine and Finite Lie Algebras and Integrable Toda Field Equations on Discrete Space-Time |
| title_full_unstemmed | Affine and Finite Lie Algebras and Integrable Toda Field Equations on Discrete Space-Time |
| title_short | Affine and Finite Lie Algebras and Integrable Toda Field Equations on Discrete Space-Time |
| title_sort | affine and finite lie algebras and integrable toda field equations on discrete space-time |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148464 |
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