{"paper":{"title":"Noncommutative homotopy algebras associated with open strings","license":"","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Hiroshige Kajiura","submitted_at":"2003-06-23T18:03:49Z","abstract_excerpt":"We discuss general properties of $A_\\infty$-algebras and their applications to the theory of open strings. The properties of cyclicity for $A_\\infty$-algebras are examined in detail. We prove the decomposition theorem, which is a stronger version of the minimal model theorem, for $A_\\infty$-algebras and cyclic $A_\\infty$-algebras and discuss various consequences of it. In particular it is applied to classical open string field theories and it is shown that all classical open string field theories on a fixed conformal background are cyclic $A_\\infty$-isomorphic to each other. The same results h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0306332","kind":"arxiv","version":2},"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"}