{"paper":{"title":"Constructions of L$_{\\infty}$ algebras and their field theory realizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP","math.RA"],"primary_cat":"math-ph","authors_text":"Dieter Lust, Matthias Traube, Olaf Hohm, Vladislav Kupriyanov","submitted_at":"2017-09-28T14:58:59Z","abstract_excerpt":"We construct L$_{\\infty}$ algebras for general `initial data' given by a vector space equipped with an antisymmetric bracket not necessarily satisfying the Jacobi identity. We prove that any such bracket can be extended to a 2-term L$_{\\infty}$ algebra on a graded vector space of twice the dimension, with the 3-bracket being related to the Jacobiator. While these L$_{\\infty}$ algebras always exist, they generally do not realize a non-trivial symmetry in a field theory. In order to define L$_{\\infty}$ algebras with genuine field theory realizations, we prove the significantly more general theor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.10004","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":""},"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"}