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arXiv · 1912.05787

Doubling pre-Lie algebra of rooted trees

Mohamed Belhaj Mohamed
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Abstract

We study the pre-Lie algebra of rooted trees $(\Cal T, \rightarrow)$ and we define a pre-Lie structure on its doubling space $(V, \leadsto)$. Also, we find the enveloping algebras of the two pre-Lie algebras denoted respectively by $(\Cal H', \star, \Gamma)$ and $(\Cal D', \bigstar, \chi)$. We prove that $(\Cal D', \bigstar, \chi)$ is a module-bialgebra on $(\Cal H', \star, \Gamma)$ and we find some relations between the two pre-Lie structures.

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BibTeXRIS

Mohamed Belhaj Mohamed. 2019-12-12. Doubling pre-Lie algebra of rooted trees. https://arxiv.org/abs/1912.05787

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