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Эта публикация цитируется в 6 научных статьях (всего в 6 статьях)
Algebraic Properties of Compatible Poisson Brackets
Pumei Zhangab a China University of Political Science and Law, 25 Xitucheng Lu, Haidian District, Beijing, 100088, China
b School of Mathematics, Loughborough University,
Loughborough, Leicestershire, LE11 3TU, United Kingdom
Аннотация:
We discuss algebraic properties of a pencil generated by two compatible Poisson
tensors $\mathcal A(x)$ and $\mathcal B(x)$. From the algebraic viewpoint this amounts to studying the properties of a pair of skew-symmetric bilinear forms $\mathcal A$ and $\mathcal B$ defined on a finite-dimensional vector space. We describe the Lie group $G_{\mathcal
P}$ of linear automorphisms of the pencil $\mathcal P = \{\mathcal A +
\lambda\mathcal B\}$. In particular, we obtain an explicit formula for the dimension of $G_{\mathcal P}$ and discuss some other
algebraic properties such as solvability and Levi – Malcev decomposition.
Ключевые слова:
compatible Poisson brackets, Jordan–Kronecker decomposition, pencils of skew symmetric matrices, bi-Hamiltonian systems.
Поступила в редакцию: 31.08.2013 Принята в печать: 26.03.2014
Образец цитирования:
Pumei Zhang, “Algebraic Properties of Compatible Poisson Brackets”, Regul. Chaotic Dyn., 19:3 (2014), 267–288
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd146 https://www.mathnet.ru/rus/rcd/v19/i3/p267
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