模和代数调和余积的稳定子是相等的
The stabilizer bitorsors of the module and algebra harmonic coproducts are equal
摘要：
在早期的工作中，我们构造了一对“Betti”和“de Rham”霍普夫代数和一对在这对上的模余代数，以及与这两种结构相关的双导子（称为“模”和“代数”稳定子双导子）。我们表明，Racinet的torsor构造出的双重洗牌和正则化关系之间的多个zeta值基本上等于“模块”稳定器bitorsor，而后者是包含在“代数”稳定器bitorsor。本文证明了“代数”稳定子与“模”稳定子的等价性。我们减少证明，以显示相关的“代数”和“模”分次李代数的平等。证明这一等式的论证涉及到“代数”李代数与线性映射核的关系，线性映射表示为三个线性映射的合成，其中一个线性映射与“模”李代数的关系，以及另一个线性映射核的离散拓扑计算.
英文摘要：
In earlier work, we constructed a pair of "Betti" and "de Rham" Hopf algebras and a pair of module-coalgebras over this pair, as well as the bitorsors related to both structures (which will be called the "module" and "algebra" stabilizer bitorsors). We showed that Racinet's torsor constructed out of the double shuffle and regularization relations between multiple zeta values is essentially equal to the "module" stabilizer bitorsor, and that the latter is contained in the "algebra" stabilizer bitorsor. In this paper, we show the equality of the "algebra" and "module" stabilizer bitorsors. We reduce the proof to showing the equality of the associated "algebra" and "module" graded Lie algebras. The argument for showing this equality involves the relation of the "algebra" Lie algebra with the kernel of a linear map, the expression of this linear map as a composition of three linear maps, the relation of one of them with the "module" Lie algebra and the computation of the kernel of the other one by discrete topology arguments.
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