Splitting of operads and Rota-Baxter operators on operads
Splitting of operads and Rota-Baxter operators on operads
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操作数的拆分和操作数上的 Rota-Baxter 算子
DOI：
10.1007/s10485-016-9431-5
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发表时间：
2017
影响因子：
0.6
通讯作者：
Li Guo
中科院分区：
文献类型：
--
作者：
Jun Pei;Chengming Bai;Li Guo
本文建立了任意代数运算符拆分的过程，推广了以往拆分代数结构的概念，从Loday拆分关联运算的树形代数到后续拆分二元操作符的树形代数。分别处理的二元操作数的后继数和三后继数通过组态的概念统一为一般操作数。应用程序提供了各种代数，代数和代数。进一步，定义了适用于所有操作数的Rota-Baxter算子的概念，首先显示了它在关联代数和李代数上下文中的重要性，然后将其推广到二元操作数。从Rota-Baxter算子到树形代数的众所周知的联系及其众多扩展被扩展为从操作数上的（相对）Rota-Baxter算子到操作数分裂的链接
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 variousn-algebras, theandalgebras. 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