Poisson brackets, Novikov-Leibniz structures and integrable Riemann hydrodynamic systems

被引：7
作者：
Artemovych, Orest D. [1 ]
Blackmore, Denis [2 ]
Prykarpatski, Anatolij K. [3 ]
机构：
[1] Cracow Univ Technol, Inst Math, PL-31155 Krakow, Poland
[2] New Jersey Inst Technol, Dept Math Sci, Newark, NJ 07102 USA
[3] AGH Univ Sci & Technol, Dept Appl Math, 30 Mickiewicz Alley, PL-30059 Krakow, Poland
来源：
JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS | 2017年 / 24卷 / 01期
关键词：
Poisson brackets; Hamiltonian operators; differential algebras; differentiations; loop-algebra; 2-cocycles; Novikov algebra; right Leibniz algebra; Riemann algebra; Riemann hydrodynamic hierarchy; integrability; NILPOTENT LIE-ALGEBRAS; AFFINE STRUCTURES; BAXTER EQUATION; DERIVATIONS; CLASSIFICATION; PREDERIVATIONS; MATRICES;
D O I：
10.1080/14029251.2016.1274114
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A general differential-algebraic approach is devised for constructing multi-component Hamiltonian operators as differentiations on suitably constructed loop Lie algebras. The related Novikov-Leibniz algebraic structures are presented and a new non-associative "Riemann" algebra is constructed, which is closely related to the infinite multi-component Riemann integrable hierarchies. A close relationship to the standard symplectic analysis techniques is also discussed.
引用
收藏
页码：41 / 72
页数：32
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