论文标题
多个小聚集体的HOPF代数和霍明型1形
Hopf algebras of multiple polylogarithms, and holomorphic 1-forms
论文作者
论文摘要
我们将其与多个多形的多形构成1形式相关联，在其域的通用Abelian覆盖物上。我们将1形与符号和变异矩阵相关联，并表明1形自然定义了与多聚凝集有关的混合霍奇结构的变化的提升。根据多个小聚集体的Goncharov的HOPF代数的变异h，可以方便地描述结果。特别是，我们表明，1形与多个多组层次的1形相关性诱导了H的Indecomposables lie Colagbra的Chevalley-Eilenberg Complex的地图与De Rham复合物的地图。
We associate to a multiple polylogarithm a holomorphic 1-form on the universal abelian cover of its domain. We relate the 1-forms to the symbol and variation matrix and show that the 1-forms naturally define a lift of the variation of mixed Hodge structure associated to a polylogarithm. The results are conveniently described in terms of a variant H of Goncharov's Hopf algebra of multiple polylogarithms. In particular, we show that the association of a 1-form to a multiple polylogarithm induces a map from the Chevalley-Eilenberg complex of the Lie coalgebra of indecomposables of H to the de Rham complex.
