Multisymplectic observable reduction using constraint triples

The purpose of this paper is to present a fully algebraic formalism for the construction and reduction of $L_{\mathrm{\infty }}$-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).