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

Orest D. Artemovych; Denis Blackmore; Anatolij K. Prykarpatski

doi:10.1080/14029251.2016.1274114

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

Orest D. Artemovych, Denis Blackmore, Anatolij K. Prykarpatski

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	41-72
Number of pages	32
Journal	Journal of Nonlinear Mathematical Physics
Volume	24
Issue number	1
DOIs	https://doi.org/10.1080/14029251.2016.1274114
State	Published - Jan 2 2017

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Keywords

2-cocycles
Hamiltonian operators
Novikov algebra
Poisson brackets
Riemann algebra
Riemann hydrodynamic hierarchy
differential algebras
differentiations
integrability
loop-algebra
right Leibniz algebra

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10.1080/14029251.2016.1274114

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abstract = "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.",

keywords = "2-cocycles, Hamiltonian operators, Novikov algebra, Poisson brackets, Riemann algebra, Riemann hydrodynamic hierarchy, differential algebras, differentiations, integrability, loop-algebra, right Leibniz algebra",

author = "Artemovych, {Orest D.} and Denis Blackmore and Prykarpatski, {Anatolij K.}",

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AU - Artemovych, Orest D.

AU - Blackmore, Denis

AU - Prykarpatski, Anatolij K.

PY - 2017/1/2

Y1 - 2017/1/2

N2 - 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.

AB - 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.

KW - 2-cocycles

KW - Hamiltonian operators

KW - Novikov algebra

KW - Poisson brackets

KW - Riemann algebra

KW - Riemann hydrodynamic hierarchy

KW - differential algebras

KW - differentiations

KW - integrability

KW - loop-algebra

KW - right Leibniz algebra

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DO - 10.1080/14029251.2016.1274114

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EP - 72

JO - Journal of Nonlinear Mathematical Physics

JF - Journal of Nonlinear Mathematical Physics

IS - 1

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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