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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2019 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2019
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210294 |
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| Cite this: | 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. |
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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 |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Bi-Hamiltonian Systems in (2+1) and Higher Dimensions Defined by Novikov Algebras |
| spellingShingle |
Bi-Hamiltonian Systems in (2+1) and Higher Dimensions Defined by Novikov Algebras Szablikowski, B.M. |
| title_short |
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_sort |
bi-hamiltonian systems in (2+1) and higher dimensions defined by novikov algebras |
| author |
Szablikowski, B.M. |
| author_facet |
Szablikowski, B.M. |
| publishDate |
2019 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/210294 |
| 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. |
| work_keys_str_mv |
AT szablikowskibm bihamiltoniansystemsin21andhigherdimensionsdefinedbynovikovalgebras |
| first_indexed |
2025-12-07T21:25:03Z |
| last_indexed |
2025-12-07T21:25:03Z |
| _version_ |
1850886275569025024 |