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Deformation of the Hopf algebra of plane posets

Loïc Foissy

Abstract

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.
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Dates and versions

hal-00687491 , version 1 (13-04-2012)
hal-00687491 , version 2 (23-11-2012)

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Loïc Foissy. Deformation of the Hopf algebra of plane posets. 2012. ⟨hal-00687491v1⟩
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