{"paper":{"title":"Higher derived brackets and homotopy algebras","license":"","headline":"","cross_cats":["math.DG","math.SG"],"primary_cat":"math.QA","authors_text":"Theodore Voronov","submitted_at":"2003-04-03T06:02:14Z","abstract_excerpt":"We give a construction of homotopy algebras based on ``higher derived brackets''. More precisely, the data include a Lie superalgebra with a projector on an Abelian subalgebra satisfying a certain axiom, and an odd element $\\Delta$. Given this, we introduce an infinite sequence of higher brackets on the image of the projector, and explicitly calculate their Jacobiators in terms of $\\Delta^2$. This allows to control higher Jacobi identities in terms of the ``order'' of $\\Delta^2$. Examples include Stasheff's strongly homotopy Lie algebras and variants of homotopy Batalin--Vilkovisky algebras. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0304038","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"}