THE DUAL OF INFINITESIMAL UNITARY HOPF ALGEBRAS AND PLANAR ROOTED FORESTS - Archive ouverte HAL Access content directly
Journal Articles International Electronic Journal of Algebra Year : 2023

THE DUAL OF INFINITESIMAL UNITARY HOPF ALGEBRAS AND PLANAR ROOTED FORESTS

Xiaomeng Wang
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Xing Gao
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Abstract

We study the infinitesimal (in the sense of Joni and Rota) bialgebra H RT of planar rooted trees introduced by Gao and Wang, 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 on its space primitive elements, which freely generates H RT .
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Dates and versions

hal-02874051 , version 1 (18-06-2020)

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Xiaomeng Wang, Loïc Foissy, Xing Gao. THE DUAL OF INFINITESIMAL UNITARY HOPF ALGEBRAS AND PLANAR ROOTED FORESTS. International Electronic Journal of Algebra, 2023, ⟨10.24330/ieja.1220707⟩. ⟨hal-02874051⟩
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