Journal of Lie Theory 26 (2016), No. 4, 1037--1067
Copyright Heldermann Verlag 2016
Products of Multisymplectic Manifolds and Homotopy Moment Maps
Carlos S. Shabazi
Institut de Physique Théorique, CEA/Saclay, 91191 Gif-sur-Yvette 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 by-product, 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
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