Résumé : There is a well-known natural functorial construction which, from a set-operad, produces a Hopf algebra. We extend this construction to the category of PROs with some extra properties. By this generalization, we retrieve, among other, the Hopf algebra of noncommutative symmetric functions in various bases and the noncommutative Faà di Bruno Hopf algebra. We also obtain new ones, as some Hopf algebras involving forests, heaps of pieces, and some kinds of combinational circuits. All these Hopf algebras are similar in a sense to the Connes-Kremier Hopf algebra. In this talk, we shall recall some background about PROs, then present the construction associating a Hopf algebra with a PRO, and finally, review some examples of applications.
|Dernière modification : samedi 13 juillet 2013||Contact : Cyril.Banderier at lipn.univ-paris13.fr|