
Journal of Lie Theory 23 (2013), No. 4, 937952 Copyright Heldermann Verlag 2013 PreLie Algebras in Positive Characteristic Ioannis Dokas Konstantinoupoleos 22, Patras 26441, Greece dokas@ucy.ac.cy In prime characteristic we introduce the notion of restricted preLie algebras. We prove in the preLie 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 preLie algebra. Thus we obtain that RotaBaxter algebras and quasitriangular algebras are restricted preLie algebras. Moreover, we prove that the free Γ(preLie)algebra is a restricted preLie algebra, where "preLie" denotes the preLie operad. Finally, we define the notion of restricted enveloping dendriform algebra and we construct a left adjoint functor for the functor ()_{ppreLie}: Dend > ppreLie . Keywords: Restricted Lie algebra, dendriform algebra, preLie algebra, algebras with divided powers over an operad. MSC: 17D25, 17B50, 18C15 [ Fulltextpdf (298 KB)] for subscribers only. 