Feuilleter
no. 2
Enveloping algebras of pre-Lie algebras of rooted trees
Mohamed Belhaj Mohamed1, 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
Confluentes Mathematici, Tome 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.

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Révisé le :
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DOI : 10.5802/cml.75
Classification : 16T10, 16T15, 16T30, 05C90, 81T17
Mots clés : 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
Licence : CC-BY-NC-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Mohamed Belhaj Mohamed. Enveloping algebras of pre-Lie algebras of rooted trees. Confluentes Mathematici, Tome 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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