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 -