Cofree Com-PreLie algebras - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2018

Cofree Com-PreLie algebras

Résumé

A Com-PreLie bialgebra is a commutative bialgebra with an extra preLie product satisfying some compatibilities with the product and the coproduct. We here give examples of cofree Com-PreLie bialgebras, including all the ones such that the preLie product is homogeneous of degree ≥ −1. We also give a graphical description of free unitary Com-PreLie algebras, explicit their canonical bialgebra structure and exhibit with the help of a rigidity theorem certain cofree quotients, including the Connes-Kreimer Hopf algebra of rooted trees. We finally prove that the dual of these bialgebras are also enveloping algebras of preLie algebras, combinatorially described.
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Dates et versions

hal-01714552 , version 1 (21-02-2018)
hal-01714552 , version 2 (08-10-2024)

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Citer

Loïc Foissy. Cofree Com-PreLie algebras. 2018. ⟨hal-01714552v2⟩
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