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Doubling pre-Lie algebra of rooted trees

Mathematics Departement, Sciences College, Taibah University, Kingdom of Saudi Arabia

Laboratoire de Mathématiques Physique, Fonctions Spéciales et Applications, Université de Sousse, Rue Lamine Abassi 4011 H. Sousse, Tunisie

E-mail Address: [email protected]

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https://doi.org/10.1142/S021949882050228XCited by:1

Abstract

We study the pre-Lie algebra of rooted trees $(𝒯, \to)$ and we define a pre-Lie structure on its doubling space $(V, ⇝)$ . Also, we find the enveloping algebras of the two pre-Lie algebras denoted, respectively, by $(ℋ^{'}, ⋆, Γ)$ and $(𝒟^{'}, ⋆, χ)$ . We prove that $(𝒟^{'}, ⋆, χ)$ is a module-bialgebra on $(ℋ^{'}, ⋆, Γ)$ and we find some relations between the two pre-Lie structures.

Communicated by S. K. Jain

Keywords:

AMSC: 05C90, 81T15, 16T05, 16T10

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Vol. 19, No. 12

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History

Received 14 May 2019

Accepted 9 October 2019

Published: 9 December 2019

Keywords

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Doubling pre-Lie algebra of rooted trees

Abstract

References

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