Pre-Lie algebras in positive characteristic

Details Pre-Lie algebras in positive characteristic Pre-Lie algebras in positive characteristic

2010-11-18

arxiv.org/abs/1011.4217v1

Mathematics

Rings and Algebras

9 pages

Scientific paper

In prime characteristic we introduce the notion of restricted pre-Lie algebra. 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. As a consequence we prove that Rota-Baxter algebras and quasitriangular algebras are restricted pre-Lie algebras. We construct a left adjoint functor to the functor $(-)_{preLie}: Dend \rightarrow preLie$. Finally, we define the notion of restricted enveloping dendriform algebra and we construct a left adjoint functor for the functor $(-)_{p-preLie}: Dend \rightarrow p-preLie$.

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