In this article, we study the insertion pre-Lie algebra of rooted trees and we construct a pre-Lie structure on its doubling space . We prove that is a left pre-Lie module on . Moreover, we describe the enveloping algebras of the two pre-Lie algebras denoted respectively by and and we show that is a module-bialgebra on . 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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Mots clés : Insertion pre-Lie algebras, Rooted Forest, Bialgebras, Enveloping algebras of pre-Lie algebras, Module-bialgebras
Mohamed Belhaj Mohamed 1, 2
@article{CML_2021__13_2_11_0, author = {Mohamed Belhaj Mohamed}, title = {Enveloping algebras of {pre-Lie} algebras of rooted trees}, journal = {Confluentes Mathematici}, pages = {11--28}, publisher = {Institut Camille Jordan}, volume = {13}, number = {2}, year = {2021}, doi = {10.5802/cml.75}, language = {en}, url = {https://cml.centre-mersenne.org/articles/10.5802/cml.75/} }
TY - JOUR AU - Mohamed Belhaj Mohamed TI - Enveloping algebras of pre-Lie algebras of rooted trees JO - Confluentes Mathematici PY - 2021 SP - 11 EP - 28 VL - 13 IS - 2 PB - Institut Camille Jordan UR - https://cml.centre-mersenne.org/articles/10.5802/cml.75/ DO - 10.5802/cml.75 LA - en ID - CML_2021__13_2_11_0 ER -
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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