Gröbner-Shirshov Basis of the Universal Enveloping Rota-Baxter Algebra of a Lie Algebra

V. Gubarev; P. Kolesnikov

doi:10.5802/jolt.973

V. Gubarev; P. Kolesnikov

Journal of Lie Theory, Volume 27 (2017) no. 3, pp. 887-905

Abstract

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 U_RB. We prove an operator analogue of the Poincaré-Birkhoff-Witt theorem for U_RB by means of Gröbner-Shirshov bases theory for Lie algebras with an additional operator.

arXiv Zbl

DOI: 10.5802/jolt.973

Classification: 17B01, 17B37
Keywords: Rota-Baxter operator, free Lie algebra, universal envelope

@article{JOLT_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},
     doi = {10.5802/jolt.973},
     zbl = {1430.17013},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.973/}
}

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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, Volume 27 (2017) no. 3, pp. 887-905. doi: 10.5802/jolt.973

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