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Reduction of $L_\infty$-Algebras of Observables on Multisymplectic Manifolds
Symmetry, integrability and geometry: methods and applications, Tome 20 (2024) Cet article a éte moissonné depuis la source Math-Net.Ru

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We develop a reduction scheme for the $L_\infty$-algebra of observables on a premultisymplectic manifold $(M,\omega)$ in the presence of a compatible Lie algebra action $\mathfrak{g}\curvearrowright M$ and subset $N\subset M$. This reproduces in the symplectic setting the Poisson algebra of observables on the Marsden–Weinstein–Meyer symplectic reduced space, whenever the reduced space exists, but is otherwise distinct from the Dirac, Śniatycki–Weinstein, and Arms–Cushman–Gotay observable reduction schemes. We examine various examples, including multicotangent bundles and multiphase spaces, and we conclude with a discussion of applications to classical field theories and quantization.
Keywords: $L_\infty$-algebras, multisymplectic manifolds, moment maps. 
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     author = {Casey Blacker and Antonio Michele Miti and Leonid Ryvkin},
     title = {Reduction of $L_\infty${-Algebras} of {Observables} on {Multisymplectic} {Manifolds}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2024},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2024_20_a60/}
}
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Casey Blacker; Antonio Michele Miti; Leonid Ryvkin. Reduction of $L_\infty$-Algebras of Observables on Multisymplectic Manifolds. Symmetry, integrability and geometry: methods and applications, Tome 20 (2024). http://geodesic.mathdoc.fr/item/SIGMA_2024_20_a60/

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