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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@misc{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).},
 arxiv = {arXiv:2506.00234},
 author = {Miti, Antonio Michele and Ryvkin, Leonid},
 eprint = {2506.00234},
 howpublished = {Preprint, {arXiv}:2506.00234 [math.{SG}] (2025)},
 keywords = {53D20,53D05,16W50},
 title = {Multisymplectic observable reduction using constraint triples},
 url = {https://arxiv.org/abs/2506.00234},
 year = {2025}
}