Doubling pre-Lie algebra of rooted trees

@article{BelhajMohamed2019DoublingPA,
  title={Doubling pre-Lie algebra of rooted trees},
  author={Mohamed Belhaj Mohamed},
  journal={Journal of Algebra and Its Applications},
  year={2019}
}
We study the pre-Lie algebra of rooted trees [Formula: see text] and we define a pre-Lie structure on its doubling space [Formula: see text]. Also, we find the enveloping algebras of the two pre-Lie algebras denoted, respectively, by [Formula: see text] and [Formula: see text]. We prove that [Formula: see text] is a module-bialgebra on [Formula: see text] and we find some relations between the two pre-Lie structures. 
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