On the Lie algebra structures connected with Hamiltonian dynamical systems
We construct the hierarchies of master symmetries constituting Virasoro-type algebras for the Hamiltonian vector fields preserving a recursion operator. Similarly, repeatedly contracting a Hamiltonian vector field with the corresponding recursion operator, we define an Abelian Lie algebra of the thus obtained hierarchy of vector fields. The approach is shown to be applicable for the Volterra and Toda lattices.
English version (Springer): Ukrainian Mathematical Journal 49 (1997), no. 5, pp 779-786.
Citation Example: Smirnov R. G. On the Lie algebra structures connected with Hamiltonian dynamical systems // Ukr. Mat. Zh. - 1997. - 49, № 5. - pp. 699–705.