有根树与对称函数：赵同态与交换六边形
Rooted trees and symmetric functions: Zhao's homomorphism and the commutative hexagon
摘要：
最近微扰量子场论的工作导致了对Connes-Kreimer霍普夫代数的大量研究。它的（分次）对偶，有根树的Grossman-Larson霍普夫代数，已经被代数学家研究过了。L.福瓦西引入了Connes-Kreimer霍普夫代数的一个非交换版本，它是自对偶的。利用作者和W. Zhao，我们描述了一个交换图表，它将上述霍普夫代数相互联系起来，并与对称函数、非交换对称函数和拟对称函数的霍普夫代数联系起来。
英文摘要：
Recent work on perturbative quantum field theory has led to much study of the Connes-Kreimer Hopf algebra. Its (graded) dual, the Grossman-Larson Hopf algebra of rooted trees, had already been studied by algebraists. L. Foissy introduced a noncommutative version of the Connes-Kreimer Hopf algebra, which turns out to be self-dual. Using some homomorphisms defined by the author and W. Zhao, we describe a commutative diagram that relates the aforementioned Hopf algebras to each other and to the Hopf algebras of symmetric functions, noncommutative symmetric functions, and quasi-symmetric functions.
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