1Institut de Physique Théorique, CEA/Saclay, 91191 Gif-sur-Yvette Cedex, France 2Dept. of Mathematics, KU Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium
Journal of Lie Theory, Tome 26 (2016) no. 4, pp. 1037-1067
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.
1
Institut de Physique Théorique, CEA/Saclay, 91191 Gif-sur-Yvette Cedex, France
2
Dept. of Mathematics, KU Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium
Carlos S. Shabazi; Marco Zambon. Products of Multisymplectic Manifolds and Homotopy Moment Maps. Journal of Lie Theory, Tome 26 (2016) no. 4, pp. 1037-1067. http://geodesic.mathdoc.fr/item/JOLT_2016_26_4_a4/
@article{JOLT_2016_26_4_a4,
author = {Carlos S. Shabazi and Marco Zambon},
title = {Products of {Multisymplectic} {Manifolds} and {Homotopy} {Moment} {Maps}},
journal = {Journal of Lie Theory},
pages = {1037--1067},
year = {2016},
volume = {26},
number = {4},
url = {http://geodesic.mathdoc.fr/item/JOLT_2016_26_4_a4/}
}
TY - JOUR
AU - Carlos S. Shabazi
AU - Marco Zambon
TI - Products of Multisymplectic Manifolds and Homotopy Moment Maps
JO - Journal of Lie Theory
PY - 2016
SP - 1037
EP - 1067
VL - 26
IS - 4
UR - http://geodesic.mathdoc.fr/item/JOLT_2016_26_4_a4/
ID - JOLT_2016_26_4_a4
ER -
%0 Journal Article
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%A Marco Zambon
%T Products of Multisymplectic Manifolds and Homotopy Moment Maps
%J Journal of Lie Theory
%D 2016
%P 1037-1067
%V 26
%N 4
%U http://geodesic.mathdoc.fr/item/JOLT_2016_26_4_a4/
%F JOLT_2016_26_4_a4
