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Grobner 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, 2017, p. 887-905.

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

Harvard

Gubarev, V & Kolesnikov, P 2017, 'Grobner 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). Grobner 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. Grobner Shirshov Basis of the Universal Enveloping Rota-Baxter Algebra of a Lie Algebra. Journal of Lie Theory. 2017;27(3):887-905.

Author

Gubarev, Vsevolod ; Kolesnikov, Pavel. / Grobner 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{321c4d3c7f3c490fa37197a18fcc1fd2,
title = "Grobner 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 U-RB. We prove an operator analogue of the Poincare-Birkhoff-Witt theorem for U-RB by means of Grobner-Shirshov bases theory for Lie algebras with an additional operator.",
keywords = "Rota-Baxter operator, free Lie algebra, universal envelope, DENDRIFORM ALGEBRAS, BASES, SYSTEMS",
author = "Vsevolod Gubarev and Pavel Kolesnikov",
year = "2017",
language = "English",
volume = "27",
pages = "887--905",
journal = "Journal of Lie Theory",
issn = "0949-5932",
publisher = "Heldermann Verlag",
number = "3",

}

RIS

TY - JOUR

T1 - Grobner Shirshov Basis of the Universal Enveloping Rota-Baxter Algebra of a Lie Algebra

AU - Gubarev, Vsevolod

AU - Kolesnikov, Pavel

PY - 2017

Y1 - 2017

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 U-RB. We prove an operator analogue of the Poincare-Birkhoff-Witt theorem for U-RB by means of Grobner-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 U-RB. We prove an operator analogue of the Poincare-Birkhoff-Witt theorem for U-RB by means of Grobner-Shirshov bases theory for Lie algebras with an additional operator.

KW - Rota-Baxter operator

KW - free Lie algebra

KW - universal envelope

KW - DENDRIFORM ALGEBRAS

KW - BASES

KW - SYSTEMS

M3 - Article

VL - 27

SP - 887

EP - 905

JO - Journal of Lie Theory

JF - Journal of Lie Theory

SN - 0949-5932

IS - 3

ER -

ID: 18738651