Geodesic
Pre-Lie Algebras in Positive Characteristic
Journal of Lie theory, Tome 23 (2013) no. 4, pp. 937-952.

Voir la notice de l'article provenant de la source Heldermann Verlag

In prime characteristic we introduce the notion of restricted pre-Lie algebras. We prove in the pre-Lie context the analogue to Jacobson's theorem for restricted Lie algebras. In particular, we prove that any dendriform algebra over a field of positive characteristic is a restricted pre-Lie algebra. Thus we obtain that Rota-Baxter algebras and quasitriangular algebras are restricted pre-Lie algebras. Moreover, we prove that the free Γ(preLie)-algebra is a restricted pre-Lie algebra, where "preLie" denotes the pre-Lie operad. Finally, we define the notion of restricted enveloping dendriform algebra and we construct a left adjoint functor for the functor (-)p-preLie: Dend --> p-preLie .
Classification : 17D25, 17B50, 18C15
Mots-clés : Restricted Lie algebra, dendriform algebra, pre-Lie algebra, algebras with divided powers over an operad 
@article{JLT_2013_23_4_JLT_2013_23_4_a2,
     author = {I. Dokas },
     title = {Pre-Lie {Algebras} in {Positive} {Characteristic}},
     journal = {Journal of Lie theory},
     pages = {937--952},
     publisher = {mathdoc},
     volume = {23},
     number = {4},
     year = {2013},
     url = {http://geodesic.mathdoc.fr/item/JLT_2013_23_4_JLT_2013_23_4_a2/}
}
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I. Dokas . Pre-Lie Algebras in Positive Characteristic. Journal of Lie theory, Tome 23 (2013) no. 4, pp. 937-952. http://geodesic.mathdoc.fr/item/JLT_2013_23_4_JLT_2013_23_4_a2/