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University of the Basque Country, Euskal Herriko Unibertsitatea
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After a brief review of some basic notions of multisymplectic geometry and a discussion of some e... more After a brief review of some basic notions of multisymplectic geometry and a discussion of some examples, special attention is paid to the concepts of Hamiltonian multivector field and Hamiltonian form on a multisymplectic manifold. In particular, it is shown that the space of equivalence classes of Hamiltonian forms, modulo closed forms, can be equipped with a graded Lie algebra structure. Next, it is demonstrated that the tangent bundle of a multisymplectic manifold is also multisymplectic, and that a locally Hamiltonian vector field is determined by a Lagrangian section of this "tangent multisymplectic structure".
After a brief review of some basic notions of multisymplectic geometry and a discussion of some e... more After a brief review of some basic notions of multisymplectic geometry and a discussion of some examples, special attention is paid to the concepts of Hamiltonian multivector field and Hamiltonian form on a multisymplectic manifold. In particular, it is shown that the space of equivalence classes of Hamiltonian forms, modulo closed forms, can be equipped with a graded Lie algebra structure. Next, it is demonstrated that the tangent bundle of a multisymplectic manifold is also multisymplectic, and that a locally Hamiltonian vector field is determined by a Lagrangian section of this "tangent multisymplectic structure".