2010/11/18 by Ioannis Dokas, Dokas, Ioannis
Mathematics · #17A32 #17B63 #18D50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1011.4217
openalex publication_date 2010/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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(\calligrapreLie)-algebra is a restricted pre-Lie algebra, where \calligrapreLie 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.