Journal of Lie Theory

no. 4
Pre-Lie Algebras in Positive Characteristic
Journal of Lie Theory, Volume 23 (2013) no. 4, pp. 937-952
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 .
DOI: 10.5802/jolt.758
Classification: 17D25, 17B50, 18C15
Keywords: Restricted Lie algebra, dendriform algebra, pre-Lie algebra, algebras with divided powers over an operad 
@article{JOLT_2013_23_4_a2,
     author = {I. Dokas},
     title = {Pre-Lie {Algebras} in {Positive} {Characteristic}},
     journal = {Journal of Lie Theory},
     pages = {937--952},
     year = {2013},
     volume = {23},
     number = {4},
     doi = {10.5802/jolt.758},
     zbl = {1285.17016},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.758/}
}
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I. Dokas. Pre-Lie Algebras in Positive Characteristic. Journal of Lie Theory, Volume 23 (2013) no. 4, pp. 937-952. doi: 10.5802/jolt.758

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