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arXiv · 1802.07642

Cofree Com-PreLie algebras

Loïc Foissy
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Abstract

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.

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Loïc Foissy. 2018-02-21. Cofree Com-PreLie algebras. https://arxiv.org/abs/1802.07642

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