ON HAMILTONIAN GROUP OF MULTISYMPLECTIC MANIFOLDS

In this paper the Hamiltonian group Ham(M, Omega) is defined for a compact k-plectic manifold (M, Omega) and it is shown that its Lie algebra is the space of equivalence classes of Hamiltonian forms, modulo closed forms. Also if psi be a multisymplectomorphism in the identity component Msymp(0)(M, Omega) of the group of multisymplectomorphisms Msymp(M, Omega), we obtain a necessary and sufficient condition under which psi belongs to Ham(M, Omega). As two consequences, we show that Hamiltonian paths are generated by Hamiltonian forms and if H(k)(M, R) = 0, then Ham(M, Omega) is equal to Msymp(0)(M, Omega).