Journal of Lie Theory 27 (2017), No. 3, 887--905
Copyright Heldermann Verlag 2017
Gröbner-Shirshov Basis of the Universal Enveloping Rota-Baxter 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 Rota-Baxter operator. The forgetful functor from this category to the category of Lie algebras has a left adjoint denoted by URB. We prove an operator analogue of the Poincaré-Birkhoff-Witt theorem for URB by means of Gröbner-Shirshov bases theory for Lie algebras with an additional operator.
Keywords: Rota-Baxter operator, free Lie algebra, universal envelope.
MSC: 17B01, 17B37
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