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

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.