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Bi-Hamiltonian Systems in (2+1) and Higher Dimensions Defined by Novikov Algebras
Symmetry, integrability and geometry: methods and applications, Tome 15 (2019) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: Novikov algebras, $(2+1)$- and $(3+1)$-dimensional integrable systems, bi-Hamiltonian structures, central extensions. 
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     author = {Bla\.zej M. Szablikowski},
     title = {Bi-Hamiltonian {Systems} in (2+1) and {Higher} {Dimensions} {Defined} by {Novikov} {Algebras}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2019},
     volume = {15},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a93/}
}
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Blażej M. Szablikowski. Bi-Hamiltonian Systems in (2+1) and Higher Dimensions Defined by Novikov Algebras. Symmetry, integrability and geometry: methods and applications, Tome 15 (2019). http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a93/

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