Cofree Com-PreLie algebras

Fuente: arXiv
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Autore principale: Foissy, Loïc
Natura: Preprint
Pubblicazione: 2018
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author Foissy, Loïc
author_facet Foissy, Loïc
contents 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 $\ge$ --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.
format Preprint
id arxiv_https___arxiv_org_abs_1802_07642
institution arXiv
publishDate 2018
record_format arxiv
spellingShingle Cofree Com-PreLie algebras
Foissy, Loïc
Rings and Algebras
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 $\ge$ --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.
title Cofree Com-PreLie algebras
topic Rings and Algebras
url https://arxiv.org/abs/1802.07642