Geometry of Hamiltonean n-vectors in Multisymplectic Field Theory

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.