Relative Rota–Baxter Operators on Groups and Hopf Algebras Научная публикация
| Журнал |
Bulletin of the Iranian Mathematical Society
ISSN: 1018-6301 , E-ISSN: 1017-060X |
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| Вых. Данные | Год: 2025, Том: 51, Номер: 4, Номер статьи : 48, Страниц : 22 DOI: 10.1007/s41980-025-00976-2 | ||||
| Ключевые слова | Hopf algebra, Cocommutative Hopf algebra, Hopf brace, Sweedler algebra, Group, Rota–Baxter operator, Relative Rota–Baxter operator | ||||
| Авторы |
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| Организации |
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Информация о финансировании (2)
| 1 | Институт математики им. С.Л. Соболева СО РАН | FWNF-2022-0009 |
| 2 | Математический центр в Академгородке | 075-15-2022-282 |
Реферат:
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.
Библиографическая ссылка:
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
Даты:
| Поступила в редакцию: | 29 авг. 2024 г. |
| Принята к публикации: | 24 февр. 2025 г. |
| Опубликована в печати: | 16 июн. 2025 г. |
| Опубликована online: | 16 июн. 2025 г. |
Идентификаторы БД:
| Web of science: | WOS:001519227600001 |
| Scopus: | 2-s2.0-105008218716 |
| OpenAlex: | W4411331925 |
Цитирование в БД:
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