Bi-Hamiltonian Systems in (2+1) and Higher Dimensions Defined by Novikov Algebras
The results from the article [Strachan I.A.B., Szablikowski B.M., Stud. Appl. Math. 133 (2014), 84-117] are extended over consideration of central extensions, allowing the introduction of additional independent variables. Algebraic conditions associated with the first-order central extension with re...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2019 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2019
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210294 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Bi-Hamiltonian Systems in (2+1) and Higher Dimensions Defined by Novikov Algebras / B.M. Szablikowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 22 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862732910948253696 |
|---|---|
| author | Szablikowski, B.M. |
| author_facet | Szablikowski, B.M. |
| citation_txt | Bi-Hamiltonian Systems in (2+1) and Higher Dimensions Defined by Novikov Algebras / B.M. Szablikowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 22 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The results from the article [Strachan I.A.B., Szablikowski B.M., Stud. Appl. Math. 133 (2014), 84-117] are extended over consideration of central extensions, allowing the introduction of additional independent variables. Algebraic conditions associated with the first-order central extension with respect to additional independent variables are derived. As a result, (2+1)- and, in principle, higher-dimensional multicomponent bi-Hamiltonian systems are constructed. Necessary classification of the central extensions for low-dimensional Novikov algebras is performed, and the theory is illustrated by significant (2+1)- and (3+1)-dimensional examples.
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| first_indexed | 2025-12-07T21:25:03Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210294 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:25:03Z |
| publishDate | 2019 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Szablikowski, B.M. 2025-12-05T09:23:36Z 2019 Bi-Hamiltonian Systems in (2+1) and Higher Dimensions Defined by Novikov Algebras / B.M. Szablikowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 22 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37K10; 17B80; 37K30 arXiv: 1906.08388 https://nasplib.isofts.kiev.ua/handle/123456789/210294 https://doi.org/10.3842/SIGMA.2019.094 The results from the article [Strachan I.A.B., Szablikowski B.M., Stud. Appl. Math. 133 (2014), 84-117] are extended over consideration of central extensions, allowing the introduction of additional independent variables. Algebraic conditions associated with the first-order central extension with respect to additional independent variables are derived. As a result, (2+1)- and, in principle, higher-dimensional multicomponent bi-Hamiltonian systems are constructed. Necessary classification of the central extensions for low-dimensional Novikov algebras is performed, and the theory is illustrated by significant (2+1)- and (3+1)-dimensional examples. I would like to thank Maciej Blaszak, Artur Sergyeyev, and Ian Strachan for various conversations concerning the theory of higher-dimensional systems and/or topics related to Novikov algebras. I would also like to thank the anonymous referees for providing to my attention the reference [11] and some important comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Bi-Hamiltonian Systems in (2+1) and Higher Dimensions Defined by Novikov Algebras Article published earlier |
| spellingShingle | Bi-Hamiltonian Systems in (2+1) and Higher Dimensions Defined by Novikov Algebras Szablikowski, B.M. |
| title | Bi-Hamiltonian Systems in (2+1) and Higher Dimensions Defined by Novikov Algebras |
| title_full | Bi-Hamiltonian Systems in (2+1) and Higher Dimensions Defined by Novikov Algebras |
| title_fullStr | Bi-Hamiltonian Systems in (2+1) and Higher Dimensions Defined by Novikov Algebras |
| title_full_unstemmed | Bi-Hamiltonian Systems in (2+1) and Higher Dimensions Defined by Novikov Algebras |
| title_short | Bi-Hamiltonian Systems in (2+1) and Higher Dimensions Defined by Novikov Algebras |
| title_sort | bi-hamiltonian systems in (2+1) and higher dimensions defined by novikov algebras |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210294 |
| work_keys_str_mv | AT szablikowskibm bihamiltoniansystemsin21andhigherdimensionsdefinedbynovikovalgebras |