A convenient criterion under which Z_2-graded operators are Hamiltonian
  We formulate a simple and convenient criterion under which skew-adjoint Z_2-graded total differential operators are Hamiltonian, provided that their images are closed under commutation in the Lie algebras of evolutionary vector fields on the infinite jet spaces for vector bundles over smooth manifolds. 
Veronique Hussin, Arthemy V. Kiselev
nlin.SI