Rota–baxter operators on unital algebras Научная публикация
| Журнал |
Moscow Mathematical Journal
ISSN: 1609-3321 |
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| Вых. Данные | Год: 2021, Том: 21, Номер: 2, Страницы: 325-364 Страниц : 40 DOI: 10.17323/1609-4514-2021-21-2-325-364 | ||||
| Ключевые слова | Faulhaber polynomial; Grassmann algebra; Matrix algebra; Rota–Baxter operator; Yang–Baxter equation | ||||
| Авторы |
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| Организации |
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Информация о финансировании (1)
| 1 | Институт математики им. С.Л. Соболева СО РАН | 0314-2019-0001 |
Реферат:
We state that all Rota–Baxter operators of nonzero weight on the Grassmann algebra over a field of characteristic zero are pro-jections on a subalgebra along another one. We show the one-to-one correspondence between the solutions of associative Yang–Baxter equation and Rota–Baxter operators of weight zero on the matrix algebra Mn(F ) (joint with P. Kolesnikov). We prove that all Rota–Baxter operators of weight zero on a unital associative (alternative, Jordan) algebraic algebra over a field of characteristic zero are nilpotent. We introduce a new invariant for an algebra A called the RB-index rb(A) as the minimal nilpotency index of Rota– Baxter operators of weight zero on A. We show that rb(Mn(F )) = 2n−1 provided that characteristic of F is zero. © 2021 Independent University of Moscow.
Библиографическая ссылка:
Gubarev V.
Rota–baxter operators on unital algebras
Moscow Mathematical Journal. 2021. V.21. N2. P.325-364. DOI: 10.17323/1609-4514-2021-21-2-325-364 WOS Scopus OpenAlex
Rota–baxter operators on unital algebras
Moscow Mathematical Journal. 2021. V.21. N2. P.325-364. DOI: 10.17323/1609-4514-2021-21-2-325-364 WOS Scopus OpenAlex
Идентификаторы БД:
| Web of science: | WOS:000663354100004 |
| Scopus: | 2-s2.0-85105351833 |
| OpenAlex: | W3155837056 |