THE DUAL OF INFINITESIMAL UNITARY HOPF ALGEBRAS AND PLANAR ROOTED FORESTS
Résumé
We study the infinitesimal (in the sense of Joni and Rota) bialgebra H RT of planar rooted trees introduced by Gao and Wang, whose coproduct is given by deletion of a vertex. We prove that its dual H * RT is isomorphic to a free non unitary algebra, and give two free generating sets. Giving H RT a second product, we make it an infinitesimal bialgebra in the sense of Loday and Ronco, which allows to explicitly construct a projector on its space primitive elements, which freely generates H RT .
Domaines
Anneaux et algèbres [math.RA]
Origine : Fichiers produits par l'(les) auteur(s)
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