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Relative Rota–Baxter Operators on Groups and Hopf Algebras Full article

Journal Bulletin of the Iranian Mathematical Society
ISSN: 1018-6301 , E-ISSN: 1017-060X
Output data Year: 2025, Volume: 51, Number: 4, Article number : 48, Pages count : 22 DOI: 10.1007/s41980-025-00976-2
Tags Hopf algebra, Cocommutative Hopf algebra, Hopf brace, Sweedler algebra, Group, Rota–Baxter operator, Relative Rota–Baxter operator
Authors Bardakov Valeriy G. 1 , Nikonov Igor M. 2
Affiliations
1 Sobolev Institute of Mathematics
2 Lomonosov Moscow State University

Funding (2)

1 Sobolev Institute of Mathematics FWNF-2022-0009
2 Mathematical Center in Akademgorodok 075-15-2022-282

Abstract: M. Goncharov introduced and studied a Rota–Baxter operator on a cocommutative Hopf algebra. In the present paper we define relative Rota–Baxter operators on an arbitrary Hopf algebra. A particular case of this definition is Goncharov’s operator. On a Hopf algebra with a relative Rota–Baxter operator we define a new associative operation and construct a new Hopf algebra and Hopf brace. Further, we construct Rota–Baxter operators of integer weights on some groups. The question on a possibility to define an operator of zero weight on groups was formulated by X. Gao, L. Guo, Y. Liu, and Z.-C. Zhu. In the last section we construct a family of two generated Hopf algebras. This family includes some known Hopf algebras, in particular, the 4-dimensional Sweedler algebra H4.
Cite: Bardakov V.G. , Nikonov I.M.
Relative Rota–Baxter Operators on Groups and Hopf Algebras
Bulletin of the Iranian Mathematical Society. 2025. V.51. N4. 48 :1-22. DOI: 10.1007/s41980-025-00976-2 WOS Scopus OpenAlex
Dates:
Submitted: Aug 29, 2024
Accepted: Feb 24, 2025
Published print: Jun 16, 2025
Published online: Jun 16, 2025
Identifiers:
Web of science: WOS:001519227600001
Scopus: 2-s2.0-105008218716
OpenAlex: W4411331925
Citing: Пока нет цитирований
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