Hamiltonian operators in graded formal calculus of variations
In this paper, continuing his previous investigations, the author considers the graded variant of the Gel'fand-Dikij formal variational calculus and generalizes some results of Gel'fand and Dorfman regarding the description of the Lie algebra of the Poisson brackets. The obtained description turns out to be connected with the polynomial Poisson algebras, considered by Sklyanin. On the other hand, from it one can derive the superanalogue theorem of Dubrovin-Novikov on the hydrodynamic Hamiltonians.
graded variant of the Gel'fand-Dikij formal variational calculus
scientific article; zbMATH DE number 3986214