Asian Journal of Mathematics and Computer Research
 

Asian Journal of Mathematics and Computer Research, ISSN No. : 2395-4205 (Print), 2395-4213 (Online), Vol.: 17, Issue.: 4

Original Research Article

HAMILTONIAN OPERATORS AND RELATED INTEGRABLE DIFFERENTIAL-ALGEBRAIC NOVIKOV-LEIBNIZ TYPE STRUCTURES

 

OREST D. ARTEMOVYCH1, DENIS BLACKMORE2 AND ANATOLIJ K. PRYKARPATSKI3*
1Department of Algebra, Institute of Mathematics and Informatics, Tadeusz Kosciuszko University of Technology, Krakow, Poland.
2Department of Mathematical Studies, NJIT, Newark, NJ, USA.
3Department of Applied Mathematics, AGH University of Science and Technology, Krakow, Poland.

Abstracts

There is devised a general differential-algebraic approach to constructing multi-component Hamiltonian operators as differentiations on suitably constructed loop Lie algebras. The related Novikov-Leibniz type algebraic structures are presented, a new non-associative "Riemann" algebra is constructed, deeply related with in nite multi-component Riemann type integrable hierarchies. The classical Poisson manifold approach, closely related with that analyzed in the present work and allowing effectively enough to construct Hamiltonian operators, is also briefly revisited.

Keywords :

Poisson brackets; Hamiltonian Operators; differenetial algebras; differentiations; loop-algebra; 2-cocycles; Novikov algebra; right Leibniz algebra; Riemann algebra; Riemann type hydrodynamic hierarchy; integrability.