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Reduced Pre-Lie Algebraic Structures, the Weak and Weakly Deformed Balinsky–Novikov Type Symmetry Algebras and Related Hamiltonian Operators
The Lie algebraic scheme for constructing Hamiltonian operators is differential-algebraically recast and an effective approach is devised for classifying the underlying algebraic structures of integrable Hamiltonian systems. Lie–Poisson analysis on the adjoint space to toroidal loop Lie algebras is employed to construct new reduced pre-Lie algebraic structures in which the …