A prelie algebra associated to a linear endomorphism and related algebraic structures

Then we study the coalgebra endomorphisms, using the graded Hopf algebra gr(H R ) associated to the filtration by deg p of [3].. Call a rooted tree t a connected and

We remind in section 2 the definition of the Connes-Moscovici Hopf alge- bra, as well as its properties and links with the Fa` a di Bruno Hopf algebra and

The study of this dendriform structure is postponed to the appendix, as well as the enumeration of partitioned trees; we also prove that free Com-Prelie algebras are free as

As explained in [8], the space generated by the double posets inherits two products and one coproduct, here denoted by m, and ∆, making it both a Hopf and an infinitesimal Hopf

The Connes-Kreimer Hopf algebra of rooted trees, introduced in [1, 6, 7, 8], is a commutative, non cocommutative Hopf algebra, its coproduct being given by admissible cuts of trees2.

we distin- guish two cases; in the first one, the Hopf subalgebra generated by the solution is isomorphic to the Faà di Bruno Hopf algebra or to the Hopf algebra of symmetric

A non-degenerate pairing and a dual basis are defined, and a combinatorial interpretation of the pairing in terms of orders on the vertices of planar forests is given.. Moreover,

We obtain in this way a 2-parameters family of Hopf subalgebras of H N CK , organized into three isomorphism classes: a first one, restricted to a polynomial ring in one variable;