Multivariable Hoffman-Ihara operators and the operad of formal power series
Multivariable Hoffman-Ihara operators and the operad of formal power series
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多变量Hoffman-Ihara算子和形式幂级数运算
DOI：
10.1016/j.jalgebra.2020.04.006
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发表时间：
2020
影响因子：
0.9
通讯作者：
Shuji Yamamoto
中科院分区：
文献类型：
--
作者：
Masataka Ono;Shin-ichiro Seki;Shuji Yamamoto;Shuji Yamamoto
我们在准洗牌代数 H 上引入了一系列多线性算子，我们称之为 Hoffman-Ihara 算子。它概括了 Hoffman 构造并由 Hoffman 和 Ihara 进一步研究的线性算子。我们证明了这些算子的组成公式，并表明该公式为洗牌和准洗牌产品的一些结果提供了统一和透明的理解。还给出了形式幂级数运算的解释。
We introduce a family of multilinear operators on a quasi-shuffle algebra H, which we call Hoffman-Ihara operators. It generalizes the linear operators constructed by Hoffman and further studied by Hoffman and Ihara. We prove the formula on the composition of these operators, and show that this formula provides a unified and transparent understanding of some results on shuffle and quasi-shuffle products. An interpretation as an action of the operad of formal power series is also given.