{"paper":{"title":"Splitting of operads and Rota-Baxter operators on operads","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.QA"],"primary_cat":"math.CT","authors_text":"Chengming Bai, Jun Pei, Li Guo","submitted_at":"2013-06-13T07:50:00Z","abstract_excerpt":"This paper establishes a uniform procedure to split the operations in any algebraic operad, generalizing previous known notions of splitting algebraic structures from the dendriform algebra of Loday that splits the associative operation to the successors that split any binary operad. Examples are provided for various $n$-associative algebras, $n$-Lie algebras, $A_\\infty$ algebras and $L_\\infty$ algebras. Further, the concept of a Rota-Baxter operator, first showing its importance in the associative and Lie algebra context and then generalized to any binary operads, is generalized to arbitrary "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3046","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"}