Rota-Baxter operators of non-scalar weights, connections with coboundary Lie bialgebra structures

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Rota-Baxter operators of non-scalar weights, connections with coboundary Lie bialgebra structures. / Goncharov, Maxim.

в: Communications in Algebra, 28.01.2025.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{913ae64aa9394971b95b45aa9b855095,

title = "Rota-Baxter operators of non-scalar weights, connections with coboundary Lie bialgebra structures",

abstract = "In the paper, we introduce the notion of a Rota-Baxter operator of a non-scalar weight. As a motivation, we show that there is a natural connection between Rota-Baxter operators of this type and structures of coboundary Lie bialgebras on a quadratic finite-dimensional Lie algebra. We find necessary and sufficient conditions for a pair (Formula presented.) to be a coboundary (triangular, quasitriangular or factorizable) Lie bialgebra in the case when (Formula presented.) is a finite-dimensional quadratic perfect Lie algebra with trivial center. Moreover, we show that some classical results on Lie bialgebras follow from the corresponding results for Rota-Baxter operators.",

keywords = "Classical Yang-Baxter equation, Lie algebra, Lie bialgebra, Rota—Baxter operator, coboundary Lie bialgebra",

author = "Maxim Goncharov",

note = "The research is supported by Russian Science Foundation (project 23-71-10005, https://rscf.ru/project/23-71-10005/).",

year = "2025",

month = jan,

day = "28",

doi = "10.1080/00927872.2025.2450032",

language = "English",

journal = "Communications in Algebra",

issn = "0092-7872",

publisher = "Taylor and Francis Ltd.",

}

RIS

TY - JOUR

T1 - Rota-Baxter operators of non-scalar weights, connections with coboundary Lie bialgebra structures

AU - Goncharov, Maxim

N1 - The research is supported by Russian Science Foundation (project 23-71-10005, https://rscf.ru/project/23-71-10005/).

PY - 2025/1/28

Y1 - 2025/1/28

N2 - In the paper, we introduce the notion of a Rota-Baxter operator of a non-scalar weight. As a motivation, we show that there is a natural connection between Rota-Baxter operators of this type and structures of coboundary Lie bialgebras on a quadratic finite-dimensional Lie algebra. We find necessary and sufficient conditions for a pair (Formula presented.) to be a coboundary (triangular, quasitriangular or factorizable) Lie bialgebra in the case when (Formula presented.) is a finite-dimensional quadratic perfect Lie algebra with trivial center. Moreover, we show that some classical results on Lie bialgebras follow from the corresponding results for Rota-Baxter operators.

AB - In the paper, we introduce the notion of a Rota-Baxter operator of a non-scalar weight. As a motivation, we show that there is a natural connection between Rota-Baxter operators of this type and structures of coboundary Lie bialgebras on a quadratic finite-dimensional Lie algebra. We find necessary and sufficient conditions for a pair (Formula presented.) to be a coboundary (triangular, quasitriangular or factorizable) Lie bialgebra in the case when (Formula presented.) is a finite-dimensional quadratic perfect Lie algebra with trivial center. Moreover, we show that some classical results on Lie bialgebras follow from the corresponding results for Rota-Baxter operators.

KW - Classical Yang-Baxter equation

KW - Lie algebra

KW - Lie bialgebra

KW - Rota—Baxter operator

KW - coboundary Lie bialgebra

UR - https://www.mendeley.com/catalogue/878a9f74-8ed8-3090-9eed-c137c46c3a9a/

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85216236474&origin=inward&txGid=8fb4b8944634164780a178051065c0f7

U2 - 10.1080/00927872.2025.2450032

DO - 10.1080/00927872.2025.2450032

M3 - Article

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

ER -

ID: 63950076