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

The nilpotent variety and invariant polynomial functions in the Hamiltonian algebra