Products of multisymplectic manifolds and homotopy moment maps

Abstract

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-infinity-embedding of the L-infinity-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-infinity-algebra, whose curvature is the multisymplectic form itself.

27 pages. Version to be published in Journal of Lie Theory

References in corpus (4)

• L-infinity algebras of local observables from higher prequantum bundles
• Higher Symplectic Geometry
• A cohomological framework for homotopy moment maps
• Strongly Homotopy Lie Algebras from Multisymplectic Geometry

Cited by in corpus (4)

• An invitation to multisymplectic geometry
• A cohomological framework for homotopy moment maps
• Reduction of $L_{\infty }$-Algebras of Observables on Multisymplectic Manifolds
• Multisymplectic actions of compact Lie groups on spheres