Abstract: In this talk we will adapt to classic Hopf algebras the theory
Aguiar on infinitesimal Hopf algebra. This will allow us to see our work on
Pieri operations on poset with a new perspective.
We introduce the concept of the Hopf algebra, HP, of a poset, P. Then
defining Pieri operations on the Poset P will naturally induce (via
universal properties) a Hopf-morphism, K, from HP to the Hopf , Qsym,
of quasi-symmetric functions.
If time allow, we will see that the peak algebra of Stembridge is then the
natural Eulerian subalgebra of Qsym.