建立在有根树上的Connes-Kreimer和Grossman-Larson霍普夫代数的关系
Relating the Connes-Kreimer and Grossman-Larson Hopf algebras built on rooted trees
摘要：
我们发现了建立在有根树上的两个霍普夫代数之间的一个关系。第一个是Connes-Kreimer Hopf代数H_R，它描述了量子场论中的某种重整化;第二个是Grossman-Larson霍普夫代数A，它是十年前由于某些“微分”和组合的原因而引入的。粗略地说，这两个霍普夫代数之间存在着对偶关系.受Connes和Kreimer为H_R引入的类似算子的启发，我们研究了A上的两个自然算子。
英文摘要：
We find a relation between two Hopf algebras built on rooted trees. The first is the Connes-Kreimer Hopf algebra H_R which describes a certain type of renormalization in quantum field theory; the second is the Grossman-Larson Hopf algebra A introduced ten years ago by some "differential" and combinatorial reasons. Roughly, the relation is the following: there exists a duality between these two Hopf algebras. We study then two natural operators on A, inspired by similar ones introduced by Connes and Kreimer for H_R.
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