Doubling bialgebras of rooted trees

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• 作者：Mohamed Belhaj Mohamed ; Dominique Manchon
• 关键词：Bialgebras ; Hopf algebras ; Comodules ; Rooted trees
• 刊名：Letters in Mathematical Physics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：107
• 期：1
• 页码：145-165
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Theoretical, Mathematical and Computational Physics; Complex Systems; Geometry; Group Theory and Generalizations;
• 出版者：Springer Netherlands
• ISSN：1573-0530
• 卷排序：107

文摘

The vector space spanned by rooted forests admits two graded bialgebra structures. The first is defined by Connes and Kreimer using admissible cuts, and the second is defined by Calaque, 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 Calaque, 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.