The bigraft algebras

Anthony Mansuy (1)

1 LMR - Laboratoire de Mathématiques de Reims

In this paper, we introduce the notion of bigraft algebra, generalizing the notions of left and right graft algebras. We give a combinatorial description of the free bigraft algebra generated by one generator and we endow this algebra with a Hopf algebra structure, and a pairing. Next, we study the Koszul dual of the bigraft operad and we give a combinatorial description of the free dual bigraft algebra generated by one generator. With the help of a rewriting method, we prove that the bigraft operad is Koszul. Finally, we define the notion of infinitesimal bigraft bialgebra and we prove a rigidity theorem for connected infinitesimal bigraft bialgebras.

Mots clés: Planar rooted trees; Koszul quadratic operads; Infinitesimal Hopf algebra

Domaines: Combinatoire [math.CO]

Anthony Mansuy. The bigraft algebras. 2012. ⟨hal-00711376⟩