Motivic fundamental group and motivic Galois group

Grothendieck-Teichmuller群是V.G.Drinfeld于1990年提出的准代数群，它是由三个特殊关系定义的：一个五边形方程和两个六边形方程。同样值得注意的是，在算术几何中，它被期望与有理整数的Motivic Galois群重合。我发现了一个意想不到的事实，实际上一个五边形方程蕴含着其他的，两个六边形方程。双重洗牌关系和结合子关系是多个Zeta值中关于有理数的两个最著名的代数关系。尽管实际上两者都被猜测会屈服。全套。在他们当中，这两个关系之间的相互关系是一个谜。P.Deligne和T.Terasoma提出了一个项目(尽管不完整)，以从后者中推断出前者的关系。我的结果之一是他们的项目最终完成了。我的方法与他们的方法大不相同，实际上是基于陈凯棠的杆件构造演算的非常简洁的想法。

The Grothendieck-Teichmuller is the pro-algebraic group introduced by V. G. Drinfeld in 1990 as a deformation group of a certain type of quantum groups, which is defined by special three relations ; one pentagon equation and two hexagon equations. It is also worthy to note that in arithmetic geometry it is expected to coincide with the motivic Galois group of rational integers. I have found the unexpected fact that actually one pentagon equation implies the others, the two hexagon equations.Double shuffle relations and associators relations are two of the most known algebraic relations over rational numbers among multiple zeta values. Though actually both are conjectured to yield. the full set. of them, an interrelationship between these two relations was a mystery. P. Deligne and T. Terasoma posed a project(though incomplete) to deduce the former relations from the latter ones. One of my results is a final completion of their project. My method is quite different from theirs and actually it is based on really concise idea on K. T. Chen's bar construction calculus.