连通双代数的Birkhoff-（Rota-Baxter）分解公式
Formulas for Birkhoff-(Rota-Baxter) decompositions related to connected bialgebra
摘要：
近年来，量子场论重整化的BPHZ算法在维数正则化后被解释为Feynmann图的霍普夫代数上的特征标的Birkhoff-（Rota-Baxter）分解（BRB），其值在Rota-Baxter代数中。本文给出了连通霍普夫代数$H$上特征标群$\mathcal{C}(H, A)$的BRB分解公式，其值在Rota-Baxter（交换）代数$A$中.为此，我们首先定义与代数$A$相关联的填充（或准混洗）霍普夫代数$A^{\tmop{st}}$。证明了对任意连通的霍普夫代数$H = k 1_H \oplus H'$，存在从$H$到$H'^{\tmop{st}}$的规范单射.该态射诱导$\mathcal{C}(A^{\tmop{st}}, A)$对$\mathcal{C}(H, A)$的作用，使得$\mathcal{C}(H, A)$中的BRB分解由$\mathcal{C}(A^{\tmop{st}}, A)$的唯一（通用）元素的作用决定。
英文摘要：
In recent years, The BPHZ algorithm for renormalization in quantum field theory has been interpreted, after dimensional regularization, as the Birkhoff-(Rota-Baxter) decomposition (BRB) of characters on the Hopf algebra of Feynmann graphs, with values in a Rota-Baxter algebra. We give in this paper formulas for the BRB decomposition in the group $\mathcal{C}(H, A)$ of characters on a connected Hopf algebra $H$, with values in a Rota-Baxter (commutative) algebra $A$. To do so we first define the stuffle (or quasi-shuffle) Hopf algebra $A^{\tmop{st}}$ associated to an algebra $A$. We prove then that for any connected Hopf algebra $H = k 1_H \oplus H'$, there exists a canonical injective morphism from $H$ to $H'^{\tmop{st}}$. This morphism induces an action of $\mathcal{C}(A^{\tmop{st}}, A)$ on $\mathcal{C}(H, A)$ so that the BRB decomposition in $\mathcal{C}(H, A)$ is determined by the action of a unique (universal) element of $\mathcal{C}(A^{\tmop{st}}, A)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
