Enveloping algebras of pre-Lie algebras of rooted trees
Confluentes Mathematici, Volume 13 (2021) no. 2, pp. 11-28.

In this article, we study the insertion pre-Lie algebra of rooted trees (𝒯,) and we construct a pre-Lie structure on its doubling space (V ˜,). We prove that V ˜ is a left pre-Lie module on 𝒯. Moreover, we describe the enveloping algebras of the two pre-Lie algebras denoted respectively by (𝒦,,ϒ) and (𝒲,,Θ) and we show that (𝒲,,Θ) is a module-bialgebra on (𝒦,,ϒ). Finally, we find some relations between the enveloping algebras of the insertion and the grafting pre-lie algebras of rooted trees.

Received:
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Accepted:
Published online:
DOI: 10.5802/cml.75
Classification: 16T10,  16T15,  16T30,  05C90,  81T17
Keywords: Insertion pre-Lie algebras, Rooted Forest, Bialgebras, Enveloping algebras of pre-Lie algebras, Module-bialgebras
Mohamed Belhaj Mohamed 1, 2

1 Laboratoire de mathématiques, physique, fonctions spéciales et applications, Université de Sousse, rue Lamine Abassi 4011 H. Sousse, Tunisie
2 Mathematics Departement, Sciences college, Taibah University, Kingdom of Saudi Arabia
License: CC-BY-NC-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Mohamed Belhaj Mohamed. Enveloping algebras of pre-Lie algebras of rooted trees. Confluentes Mathematici, Volume 13 (2021) no. 2, pp. 11-28. doi : 10.5802/cml.75. https://cml.centre-mersenne.org/articles/10.5802/cml.75/

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