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Gröbner-Shirshov basis of the universal enveloping Rota-Baxter algebra of a Lie algebra. / Gubarev, Vsevolod; Kolesnikov, Pavel.

In: Journal of Lie Theory, Vol. 27, No. 3, 01.01.2017, p. 887-905.

Research output: Contribution to journal › Article › peer-review

Harvard

Gubarev, V & Kolesnikov, P 2017, 'Gröbner-Shirshov basis of the universal enveloping Rota-Baxter algebra of a Lie algebra', Journal of Lie Theory, vol. 27, no. 3, pp. 887-905.

APA

Gubarev, V., & Kolesnikov, P. (2017). Gröbner-Shirshov basis of the universal enveloping Rota-Baxter algebra of a Lie algebra. Journal of Lie Theory, 27(3), 887-905.

Vancouver

Gubarev V, Kolesnikov P. Gröbner-Shirshov basis of the universal enveloping Rota-Baxter algebra of a Lie algebra. Journal of Lie Theory. 2017 Jan 1;27(3):887-905.

Author

Gubarev, Vsevolod ; Kolesnikov, Pavel. / Gröbner-Shirshov basis of the universal enveloping Rota-Baxter algebra of a Lie algebra. In: Journal of Lie Theory. 2017 ; Vol. 27, No. 3. pp. 887-905.

BibTeX

@article{082c887d02a74d1dab05ad1f9e60203b,
title = "Gr{\"o}bner-Shirshov basis of the universal enveloping Rota-Baxter algebra of a Lie algebra",
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 one denoted by URB. We prove an operator analogue of the Poincar{\'e}-Birkhoff-Witt theorem for URB by means of Gr{\"o}bner-Shirshov bases theory for Lie algebras with an additional operator.",
keywords = "Free Lie algebra, Rota-Baxter operator, Universal envelope",
author = "Vsevolod Gubarev and Pavel Kolesnikov",
year = "2017",
month = jan,
day = "1",
language = "English",
volume = "27",
pages = "887--905",
journal = "Journal of Lie Theory",
issn = "0949-5932",
publisher = "Heldermann Verlag",
number = "3",

}

RIS

TY - JOUR

T1 - Gröbner-Shirshov basis of the universal enveloping Rota-Baxter algebra of a Lie algebra

AU - Gubarev, Vsevolod

AU - Kolesnikov, Pavel

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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 one 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.

AB - 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 one 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.

KW - Free Lie algebra

KW - Rota-Baxter operator

KW - Universal envelope

UR - http://www.scopus.com/inward/record.url?scp=85014195378&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85014195378

VL - 27

SP - 887

EP - 905

JO - Journal of Lie Theory

JF - Journal of Lie Theory

SN - 0949-5932

IS - 3

ER -

ID: 10277986