标题： 数论、物理与拓扑中的三个Hopf代数及其共同背景I：运算与单纯形方面 显示英文标题

标题： Three Hopf algebras from number theory, physics & topology, and their common background I: operadic & simplicial aspects

摘要： 我们考虑数论、数学物理和代数拓扑中三个先验完全不同的Hopf代数设定。这些是Goncharov关于多重zeta值的Hopf代数、Connes-Kreimer关于重整化的Hopf代数，以及Baues构造的用于研究二重回路空间的Hopf代数。我们表明，通过考虑单纯对象、带乘法的co-operad和Feynman范畴，这些例子可以在最高层面上依次统一起来。这些考量为新的构造以及在广泛共同框架下重新解释已知构造打开了大门，并通过例子逐步呈现了这一框架。在这两篇论文的第一部分，我们集中讨论单纯性和operad方面的内容。 显示英文摘要

摘要： We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebra of Goncharov for multiple zeta values, that of Connes-Kreimer for renormalization, and a Hopf algebra constructed by Baues to study double loop spaces. We show that these examples can be successively unified by considering simplicial objects, co-operads with multiplication and Feynman categories at the ultimate level. These considerations open the door to new constructions and reinterpretations of known constructions in a large common framework, which is presented step-by-step with examples throughout. In this first part of two papers, we concentrate on the simplicial and operadic aspects.