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Rota-Baxter operators on cocommutative Hopf algebras. / Goncharov, Maxim.

In: Journal of Algebra, Vol. 582, 15.09.2021, p. 39-56.

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

Harvard

Goncharov, M 2021, 'Rota-Baxter operators on cocommutative Hopf algebras', Journal of Algebra, vol. 582, pp. 39-56. https://doi.org/10.1016/j.jalgebra.2021.04.024

APA

Goncharov, M. (2021). Rota-Baxter operators on cocommutative Hopf algebras. Journal of Algebra, 582, 39-56. https://doi.org/10.1016/j.jalgebra.2021.04.024

Vancouver

Goncharov M. Rota-Baxter operators on cocommutative Hopf algebras. Journal of Algebra. 2021 Sept 15;582:39-56. doi: 10.1016/j.jalgebra.2021.04.024

Author

Goncharov, Maxim. / Rota-Baxter operators on cocommutative Hopf algebras. In: Journal of Algebra. 2021 ; Vol. 582. pp. 39-56.

BibTeX

@article{2040b64cd1324b49842c9c56cb1b8c85,
title = "Rota-Baxter operators on cocommutative Hopf algebras",
abstract = "In this paper, we introduce and study the notion of a Rota-Baxter operator on a cocommutative Hopf algebra that generalizes notions of a Rota-Baxter operator on a group and a Rota-Baxter operator of weight 1 on a Lie algebra. We show that every Rota-Baxter operator (of weight 1) on a Lie algebra g (resp., on a group G) can be uniquely extended to a Rota-Baxter operator on the universal enveloping algebra U(g) (resp., on the group algebra F[G]).",
keywords = "Cocommutative Hopf algebra, Rota-Baxter group, Rota-Baxter Lie algebra, Rota—Baxter operator",
author = "Maxim Goncharov",
note = "Funding Information: The work was supported by Russian Scientific Fond (project N 19-11-00039). Publisher Copyright: {\textcopyright} 2021 Elsevier Inc. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",
year = "2021",
month = sep,
day = "15",
doi = "10.1016/j.jalgebra.2021.04.024",
language = "English",
volume = "582",
pages = "39--56",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press Inc.",

}

RIS

TY - JOUR

T1 - Rota-Baxter operators on cocommutative Hopf algebras

AU - Goncharov, Maxim

N1 - Funding Information: The work was supported by Russian Scientific Fond (project N 19-11-00039). Publisher Copyright: © 2021 Elsevier Inc. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/9/15

Y1 - 2021/9/15

N2 - In this paper, we introduce and study the notion of a Rota-Baxter operator on a cocommutative Hopf algebra that generalizes notions of a Rota-Baxter operator on a group and a Rota-Baxter operator of weight 1 on a Lie algebra. We show that every Rota-Baxter operator (of weight 1) on a Lie algebra g (resp., on a group G) can be uniquely extended to a Rota-Baxter operator on the universal enveloping algebra U(g) (resp., on the group algebra F[G]).

AB - In this paper, we introduce and study the notion of a Rota-Baxter operator on a cocommutative Hopf algebra that generalizes notions of a Rota-Baxter operator on a group and a Rota-Baxter operator of weight 1 on a Lie algebra. We show that every Rota-Baxter operator (of weight 1) on a Lie algebra g (resp., on a group G) can be uniquely extended to a Rota-Baxter operator on the universal enveloping algebra U(g) (resp., on the group algebra F[G]).

KW - Cocommutative Hopf algebra

KW - Rota-Baxter group

KW - Rota-Baxter Lie algebra

KW - Rota—Baxter operator

UR - http://www.scopus.com/inward/record.url?scp=85105547901&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2021.04.024

DO - 10.1016/j.jalgebra.2021.04.024

M3 - Article

AN - SCOPUS:85105547901

VL - 582

SP - 39

EP - 56

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -

ID: 28555516