  Multisymplectic geometry - which originates from the well known de
Donder-Weyl theory - is a natural framework for the study of classical field
theories. Recently, two algebraic structures have been put forward to encode a
given theory algebraically. Those structures are formulated on finite
dimensional spaces, which seems to be surprising at first. In this article, we
investigate the correspondence of Hamiltonian functions and certain
antisymmetric tensor products of vector fields. The latter turn out to be the
proper generalisation of the Hamiltonian vector fields of classical mechanics.
Thus we clarify the algebraic description of solutions of the field equations.
