Deformation of the Hopf algebra of plane posets

Loïc Foissy (1)

1 LMR - Laboratoire de Mathématiques de Reims

We describe and study a four parameters deformation of the two products and the coproduct of the Hopf algebra of plane posets. We obtain a family of braided Hopf algebras, generally self-dual. We also prove that in a particular case (when the second parameter goes to zero and the first and third parameters are equal), this deformation is isomorphic, as a self-dual braided Hopf algebra, to a deformation of the Hopf algebra of free quasi-symmetric functions.

Mots clés: Plane posets; Deformation; Braided Hopf algebras; Self- duality

Domaines: Anneaux et algèbres [math.RA]

Loïc Foissy. Deformation of the Hopf algebra of plane posets. European Journal of Combinatorics, 2014. ⟨hal-00687491v2⟩