有根树的二重双代数
Doubling bialgebras of rooted trees
摘要：
有根森林所张成的向量空间具有两个分次双代数结构。第一种是由A. Connes和D. Kreimer利用容许截集定义了第二个问题，第二个问题由D.卡拉克湾Ebrahimi-Fard和第二作者使用树的收缩。在这篇文章中，我们定义了这两个空间的加倍。我们在这些相互作用的空间上构造了两个双代数结构，并通过对偶化得到了两个相关的结合积。我们还证明了这两个双代数验证了一个类似于D验证的图的交换图表。卡拉克湾Ebrahimi-Fard和第二作者在有根树霍普夫代数的情况下，以及第二作者在无圈定向图的情况下，得到了一些新的结果.
英文摘要：
The vector space spanned by rooted forests admits two graded bialgebra structures. The first is defined by A. Connes and D. Kreimer using admissible cuts, and the second is defined by D. Calaque, K. Ebrahimi-Fard and the second author using contraction of trees. In this article we define the doubling of these two spaces. We construct two bialgebra structures on these spaces which are in interaction, as well as two related associative products obtained by dualization. We also show that these two bialgebras verify a commutative diagram similar to the diagram verified D. Calaque, K. Ebrahimi-Fard and the second author in the case of rooted trees Hopf algebra, and by the second author in the case of cycle free oriented graphs.
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