  Premet has conjectured that the nilpotent variety of any finite-dimensional
restricted Lie algebra is an irreducible variety. In this paper, we prove this
conjecture in the case of Hamiltonian Lie algebra. and show that its nilpotent
variety is normal and a complete intersection. In addition, we generalize the
Chevalley Restriction theorem to Hamiltonian Lie algebra. Accordingly, we give
the generators of the invariant polynomial ring.
