Nantel Bergeron
York University
Abstract: In this talk we will adapt to classic Hopf algebras the theory
of
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.