
Journal of Lie Theory 26 (2016), No. 4, 10371067 Copyright Heldermann Verlag 2016 Products of Multisymplectic Manifolds and Homotopy Moment Maps Carlos S. Shabazi Institut de Physique Théorique, CEA/Saclay, 91191 GifsurYvette Cedex, France carlos.shabazi@cea.fr Marco Zambon Dept. of Mathematics, KU Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium marco.zambon@wis.kuleuven.be Multisymplectic geometry admits an operation that has no counterpart in symplectic geometry, namely, taking the product of two multisymplectic manifolds endowed with the wedge product of the multisymplectic forms. We show that there is an L_{∞}embedding of the L_{∞}algebra of observables of the individual factors into the observables of the product, and that homotopy moment maps for the individual factors induce a homotopy moment map for the product. As a byproduct, we associate to every multisymplectic form a curved L_{∞}algebra, whose curvature is the multisymplectic form itself. Keywords: Multisymplectic manifold, moment map, strong homotopy Lie algebra. MSC: 53D20 [ Fulltextpdf (646 KB)] for subscribers only. 