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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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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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| ISSN: | 1815-0659 |