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

Vsevolod Gubarev; Pavel Kolesnikov

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

Section of Algebra and Mathematical Logic

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

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.

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 - 2017

Keywords

Rota-Baxter operator
free Lie algebra
universal envelope
DENDRIFORM ALGEBRAS
BASES
SYSTEMS

Cite this

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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",

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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 -

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

Abstract

Keywords

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