abstract: The purpose of this paper is to present a fully algebraic formalism for the construction and reduction of $L_\infty$-algebras of observables inspired by multisymplectic geometry, using Gerstenhaber algebras, BV-modules, and the constraint triple formalism. In the "geometric case", we reconstruct and conceptually explain the recent results of arXiv:2206.03137(3).

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@article{Miti-Multisymplectic-observable-reduction-2025,
 abstract = {The purpose of this paper is to present a fully algebraic formalism for the
construction and reduction of $L_\infty$-algebras of observables inspired by
multisymplectic geometry, using Gerstenhaber algebras, BV-modules, and the
constraint triple formalism. In the "geometric case", we reconstruct and
conceptually explain the recent results of arXiv:2206.03137(3).},
 author = {Miti, Antonio Michele and Ryvkin, Leonid},
 doi = {10.1016/j.difgeo.2025.102272},
 eprint = {2506.00234},
 issn = {0926-2245},
 journal = {Differential Geometry and its Applications},
 keywords = {53D20,53D05,16W50},
 pages = {102272},
 title = {Multisymplectic observable reduction using constraint triples},
 volume = {100},
 year = {2025}
}