Journal of Nonlinear Mathematical Physics

Volume 24, Issue 1, December 2016, Pages 41 - 72

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

Authors
Orest D. Artemovych
Institute of Mathematics, Cracow University of Technology, 31-155 Kraków, Poland
Denis Blackmore
Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102-1982, USA
Anatolij K. Prykarpatski
Department of Applied Mathematics, AGH University of Science and Technology, 30 Mickiewicz Alley, 30-059 Kraków, Poland,pryk.anat@cybergal.com
Received 4 September 2016, Accepted 22 November 2016, Available Online 6 January 2021.
DOI
10.1080/14029251.2016.1274114How to use a DOI?
Keywords
Poisson brackets; Hamiltonian operators; differential algebras; differentiations; loop-algebra; 2-cocycles; Novikov algebra; right Leibniz algebra; Riemann algebra; Riemann hydrodynamic hierarchy; integrability
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.

Copyright
© 2017 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
24 - 1
Pages
41 - 72
Publication Date
2021/01/06
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2016.1274114How to use a DOI?
Copyright
© 2017 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Orest D. Artemovych
AU  - Denis Blackmore
AU  - Anatolij K. Prykarpatski
PY  - 2021
DA  - 2021/01/06
TI  - Poisson brackets, Novikov-Leibniz structures and integrable Riemann hydrodynamic systems
JO  - Journal of Nonlinear Mathematical Physics
SP  - 41
EP  - 72
VL  - 24
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2016.1274114
DO  - 10.1080/14029251.2016.1274114
ID  - Artemovych2021
ER  -