2014/11/09 by Leonid Ryvkin, Tilmann Wurzbacher · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Covariant transformation #Homotopy #Homotopy and Cohomology in Algebraic Topology #Infinitesimal #Lie algebra #Lie group #Manifold (fluid mechanics) #Simple (philosophy) #Symplectic geometry #math-ph #math.DG #math.MP
paper · pdf · doi:10.1016/j.difgeo.2015.04.001
published as Differential geometry and its applications 41 (2015), 1-11
arxiv created 2014/11/09 · openalex publication_date 2015/04/17 · openalex created_date 2016/06/24 · arxiv updated 2016/10/28 · openalex updated_date 2026/08/05
Given a multisymplectic manifold (M,ω) and a Lie algebra \frakg acting on it by infinitesimal symmetries, Fregier-Rogers-Zambon define a homotopy (co-)moment as an L∞-algebra-homomorphism from \frakg to the observable algebra L(M,ω) associated to (M,ω), in analogy with and generalizing the notion of a co-moment map in symplectic geometry. We give a cohomological characterization of existence and unicity for homotopy co-moment maps and show its utility in multisymplectic geometry by applying it to special cases as exact multisymplectic manifolds and simple Lie groups and by deriving from it existence results concerning partial co-moment maps, as e.g. covariant multimomentum maps and multi-moment maps.