4 papers
On the pre-Lie algebra of specified Feynman graphs
Mohamed Belhaj Mohamed
We study the pre-Lie algebra of specified Feynman graphs $\wt{V}_{\Cal T}$ and we define a pre-Lie structure on its doubling space $\wt{\Cal F}_{\Cal T}$. We prove that $\wt{\Cal F…
Shuffle quadri-algebra and concatenation
Mohamed Belhaj Mohamed, Dominique Manchon
In this article, we study the shuffle quadri-algebra H. We prove the existence of some relations between quadri-algebra laws which constitute shuffle product, the concatenation pro…
Doubling bialgebras of graphs and feynman rules
Mohamed Belhaj Mohamed
In this article, we define a doubling procedure for the bialgebra of specified Feynman graphs introduced in a previous paper \cite {DMB}. This is the vector space generated by the…
Doubling bialgebras of rooted trees
Mohamed Belhaj Mohamed, Dominique Manchon
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…