{"paper":{"title":"Reduction of $L_\\infty$-Algebras of Observables on Multisymplectic Manifolds","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.DG","authors_text":"Antonio Michele Miti, Casey Blacker, Leonid Ryvkin","submitted_at":"2022-06-07T09:21:37Z","abstract_excerpt":"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, \\'Sniatycki-Weinstein, and Arms-Cushman-Gotay observable reduction schemes. We examine various examples, including multicotangent bundles and multiphase spaces, a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.03137","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2206.03137/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}