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/).
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 -