{"paper":{"title":"Cohomology theories for homotopy algebras and noncommutative geometry","license":"","headline":"","cross_cats":["math.AG","math.KT"],"primary_cat":"math.QA","authors_text":"Alastair Hamilton, Andrey Lazarev","submitted_at":"2007-07-26T15:38:53Z","abstract_excerpt":"This paper builds a general framework in which to study cohomology theories of strongly homotopy algebras, namely $A_\\infty, C_\\infty$ and $L_\\infty$-algebras. This framework is based on noncommutative geometry as expounded by Connes and Kontsevich. The developed machinery is then used to establish a general form of Hodge decomposition of Hochschild and cyclic cohomology of $C_\\infty$-algebras. This generalizes and puts in a conceptual framework previous work by Loday and Gerstenhaber-Schack."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.3937","kind":"arxiv","version":1},"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"}