The dual of infinitesimal unitary Hopf algebras and planar rooted forests

Authors : Xiaomeng WANG, Loic FOISSY, Xing GAO

Pages : 178-204

Doi:10.24330/ieja.1220707

View : 12 | Download : 9

Publication Date : 2023-01-09

Article Type : Research Paper

Abstract :We study the infinitesimal insert ignore into journalissuearticles values(in the sense of Joni and Rota); bialgebra $H_{RT}$ of planar rooted trees introduced in a previous work of two of the authors, whose coproduct is given by deletion of a vertex. We prove that its dual $H_{RT}^*$ is isomorphic to a free non unitary algebra, and give two free generating sets. Giving $H_{RT}$ a second product, we make it an infinitesimal bialgebra in the sense of Loday and Ronco, which allows to explicitly construct a projector onto its space of primitive elements, which freely generates $H_{RT}$.
Keywords : Infinitesimal bialgebra, planar rooted trees, graftings, 1 cocycle