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

Vsevolod Gubarev; Pavel Kolesnikov

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

Vsevolod Gubarev, Pavel Kolesnikov

Section of Algebra and Mathematical Logic

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

3 Citations (Scopus)

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

Original language	English
Pages (from-to)	887-905
Number of pages	19
Journal	Journal of Lie Theory
Volume	27
Issue number	3
Publication status	Published - 1 Jan 2017

Keywords

Free Lie algebra
Rota-Baxter operator
Universal envelope

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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",

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language = "English",

volume = "27",

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journal = "Journal of Lie Theory",

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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

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M3 - Article

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VL - 27

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EP - 905

JO - Journal of Lie Theory

JF - Journal of Lie Theory

SN - 0949-5932

IS - 3

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