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arXiv · 1906.08388

Bi-Hamiltonian Systems in (2+1) and Higher Dimensions Defined by Novikov Algebras

Błażej M. Szablikowski
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Abstract

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 introducing of additional independent variables. Algebraic conditions associated to the first-order central extension with respect to additional independent variables are derived. As 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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Błażej M. Szablikowski. 2019-06-19. Bi-Hamiltonian Systems in (2+1) and Higher Dimensions Defined by Novikov Algebras. https://doi.org/10.3842/sigma.2019.094

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