
Journal of Lie Theory 27 (2017), No. 3, 887905 Copyright Heldermann Verlag 2017 GröbnerShirshov Basis of the Universal Enveloping RotaBaxter Algebra of a Lie Algebra Vsevolod Gubarev Sobolev Institute of Mathematics, Akad. Koptyug prosp. 4, Novosibirsk 630090, Russia and: Novosibirsk State University, Pirogov str. 2, Novosibirsk 630090, Russia wsewolod89@gmail.com Pavel Kolesnikov Sobolev Institute of Mathematics, Akad. Koptyug prosp. 4, Novosibirsk 630090, Russia pavelsk@math.nsc.ru We consider Lie algebras equipped with a RotaBaxter operator. The forgetful functor from this category to the category of Lie algebras has a left adjoint denoted by U_{RB}. We prove an operator analogue of the PoincaréBirkhoffWitt theorem for U_{RB} by means of GröbnerShirshov bases theory for Lie algebras with an additional operator. Keywords: RotaBaxter operator, free Lie algebra, universal envelope. MSC: 17B01, 17B37 [ Fulltextpdf (315 KB)] for subscribers only. 