Faà di Bruno subalgebras of the Hopf algebras of the Hopf algebras of planar trees - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2007

Faà di Bruno subalgebras of the Hopf algebras of the Hopf algebras of planar trees

Loïc Foissy

Résumé

We describe a 2-parameters family of Hopf subalgebras of the non-commutative Connes-Kreimer Hopf algebra of planar rooted trees. They are organized into three isomorphism classes: a first one, restricted to a polynomial ring in one variable; a second one, restricted to the Hopf subalgebra of ladders, isomorphic to the Hopf algebra of quasi-symmetric functions; a last (infinite) one, which gives a non-commutative version of the Faà di Bruno Hopf algebra. By taking the quotient, the last classe gives an infinite set of embeddings of the Faà di Bruno algebra into the Connes-Kreimer Hopf algebra of rooted trees. Moreover, we give an embedding of the free Faà di Bruno Hopf algebra on N variables into a Hopf algebra of decorated rooted trees, together with a non commutative version of this embedding.
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Dates et versions

hal-00160827 , version 1 (09-07-2007)
hal-00160827 , version 2 (28-11-2007)

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Loïc Foissy. Faà di Bruno subalgebras of the Hopf algebras of the Hopf algebras of planar trees. 2007. ⟨hal-00160827v1⟩
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