Hamilton Operators and Related Integrable Differential Algebraic Novikov–Leibniz Type Structures

Abstract

There is devised a general differential-algebraic approach to constructing multi-component Hamiltonian operators as classical Lie–Poisson structures on the suitably constructed adjacent loop Lie co-algebras. The related Novikov–Leibniz type algebraic structures are derived, a new nonassociative right Leibniz and Riemann algebra is constructed, deeply related with infinite multi-component Riemann type integrable hydrodynamic hierarchies.