{"paper":{"title":"On the deformation complex of homotopy affine actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.AT","authors_text":"Alexandre Quesney, Eduardo Hoefel, Muriel Livernet","submitted_at":"2016-12-19T20:53:39Z","abstract_excerpt":"An affine action of an associative algebra $A$ on a vector space $V$ is an algebra morphism $A \\to V \\rtimes {\\rm End}(V)$, where $V$ is a vector space and $V \\rtimes {\\rm End}(V)$ is the algebra of affine transformations of $V$. The one dimensional version of the Swiss-Cheese operad, denoted ${\\mathrm{\\bf{sc}}}_1$, is the operad that governs affine actions of associative algebras. This operad is Koszul and admits a minimal model denoted by $({\\mathrm{\\bf{sc}}}_1)_\\infty$. Algebras over this minimal model are called Homotopy Affine Actions, they consist of an $A_\\infty$-morphism $A \\to V \\rtim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06363","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"}