Splitting of Operads and Rota-Baxter Operators on Operads

Jun Pei, Chengming Bai, Li Guo

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


This paper establishes a procedure that splits the operations in any algebraic operad, generalizing previous notions of splitting algebraic structures, from the dendriform algebra of Loday splitting the associative operation to the successors splitting binary operads. The separately treated bisuccessor and trisuccessor for binary operads are unified for general operads through the notion of configuration. Applications are provided for various n-algebras, the A and L algebras. Further, the concept of a Rota-Baxter operator, first showing its importance in the associative and Lie algebra contexts and then generalized to binary operads, is defined for all operads. The well-known connection from Rota-Baxter operators to dendriform algebras and its numerous extensions are expanded as the link from (relative) Rota-Baxter operators on operads to splittings of the operads.

Original languageEnglish (US)
Pages (from-to)505-538
Number of pages34
JournalApplied Categorical Structures
Issue number4
StatePublished - Aug 1 2017

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)
  • Algebra and Number Theory


  • A algebra
  • Dendriform algebra
  • L algebra
  • Operad
  • Pre-Lie algebra
  • Rota-Baxter operator
  • Splitting
  • Successor
  • n-algebra


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