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Doubling pre-Lie algebra of rooted trees

    We study the pre-Lie algebra of rooted trees (𝒯,) 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 (,,Γ) and (𝒟,,χ). We prove that (𝒟,,χ) is a module-bialgebra on (,,Γ) and we find some relations between the two pre-Lie structures.

    Communicated by S. K. Jain

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


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