
Journal of Lie Theory 30 (2020), No. 1, 223238 Copyright Heldermann Verlag 2020 PoincaréBirkhoffWitt Theorem for PreLie and PostLie Algebras Vsevolod Gubarev Sobolev Institute of Mathematics, 630090 Novosibirsk, Russia and: Faculty of Mathematics, University of Vienna, 1090 Vienna, Austria wsewolod89@gmail.com We construct the universal enveloping preassociative and postassociative algebra for a preLie and a postLie algebra, respectively. We show that the pairs (preLie, preAs) and (postLie, postAs) are PoincaréBirkhoffWittpairs; for the first this is a reproof of the result of V. Dotsenko and P. Tamaroff. Keywords: RotaBaxter operator, GroebnerShirshov basis, preLie algebra, postLie algebra, preassociative algebra, dendriform algebra, postassociative algebra. MSC: 16W99,17D25. [ Fulltextpdf (158 KB)] for subscribers only. 