Geodesic
Gröbner-Shirshov Basis of the Universal Enveloping Rota-Baxter Algebra of a Lie Algebra
Journal of Lie theory, Tome 27 (2017) no. 3, pp. 887-905
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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.
Classification : 17B01, 17B37
Mots-clés : Rota-Baxter operator, free Lie algebra, universal envelope 
@article{JLT_2017_27_3_JLT_2017_27_3_a11,
     author = {V. Gubarev and P. Kolesnikov},
     title = {Gr\"obner-Shirshov {Basis} of the {Universal} {Enveloping} {Rota-Baxter} {Algebra} of a {Lie} {Algebra}},
     journal = {Journal of Lie theory},
     pages = {887--905},
     year = {2017},
     volume = {27},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JLT_2017_27_3_JLT_2017_27_3_a11/}
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V. Gubarev; P. Kolesnikov. Gröbner-Shirshov Basis of the Universal Enveloping Rota-Baxter Algebra of a Lie Algebra. Journal of Lie theory, Tome 27 (2017) no. 3, pp. 887-905. http://geodesic.mathdoc.fr/item/JLT_2017_27_3_JLT_2017_27_3_a11/