Geodesic
Gröbner-Shirshov Basis of the Universal Enveloping Rota-Baxter Algebra of a Lie Algebra
Vsevolod Gubarev1, 2 ; Pavel Kolesnikov1
1Sobolev Institute of Mathematics, Akad. Koptyug prosp. 4, Novosibirsk 630090, Russia
2Novosibirsk State University, Pirogov str. 2, Novosibirsk 630090, Russia
Journal of Lie Theory, Tome 27 (2017) no. 3, pp. 887-905

Voir la notice de l'article provenant de la source Heldermann Verlag

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

Vsevolod Gubarev  1 , 2   ; Pavel Kolesnikov  1

1 Sobolev Institute of Mathematics, Akad. Koptyug prosp. 4, Novosibirsk 630090, Russia
2 Novosibirsk State University, Pirogov str. 2, Novosibirsk 630090, Russia 
Vsevolod Gubarev; Pavel 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/JOLT_2017_27_3_a11/
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     author = {Vsevolod Gubarev and Pavel 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/JOLT_2017_27_3_a11/}
}
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