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 |
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| 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 |
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| Affiliations |
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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
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 |