关联器剖析
Anatomy of an associator
摘要：
研究了一类由带极点的双洗牌方程的解所定义的李代数，构造了这些方程在所有权和深度下的显式解族。这些提供了写下“zeta元素”的通用坐标：整数上的混合Tate动机的动机伽罗瓦群的李代数的生成元的图像。我们希望类似的陈述也适用于关联器。特别地，这些坐标编码多个zeta值之间的代数关系，并且使得能够将当前使用的用于例如权重$\leq 13$中的多个zeta值之间的关系的表压缩一千倍。李代数和团体在这里研究形成一个大的代数结构的一部分，这是有关的工作埃卡尔的演算模具，也涉及到理论的普遍混合椭圆动机，和模形式的充分模群。
英文摘要：
We study some Lie algebras defined by solutions to the double shuffle equations with poles and construct families of explicit solutions to these equations in all weights and depths. These provide universal coordinates in which to write down `zeta elements': the images of generators of the Lie algebra of the motivic Galois group of mixed Tate motives over the integers. We expect that a similar statement holds for associators. In particular, these coordinates encode algebraic relations between multiple zeta values, and enable one to compress the currently used tables for relations between multiple zeta values in, for example, weights $\leq 13$, already by a factor of a thousand. The Lie algebras and groups studied here form part of a large algebraic structure which is related to the work of Ecalle on the calculus of moulds, and also related to the theory of universal mixed elliptic motives, and modular forms for the full modular group.
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