Spectrum of Rota - Baxter Operators Научная публикация
| Журнал |
International Journal of Algebra and Computation
ISSN: 0218-1967 , E-ISSN: 1793-6500 |
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| Вых. Данные | Год: 2025, Страницы: 1-26 Страниц : 26 DOI: 10.1142/s0218196725500195 | ||||
| Ключевые слова | Rota–Baxter operator; matrix algebra; associative Yang–Baxter equation; Rota–Baxter module | ||||
| Авторы |
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Реферат:
Rota–Baxter operators have been studied since 1960, and there are lots of their applications in mathematical physics, number theory, and noncommutative geometry. We state a surprisingly general property of such operators: the spectrum of every Rota–Baxter operator of weight λ on a finite-dimensional unital (not necessarily associative) algebra is a subset of {0,−λ}. We even extend this result to the case of infinite-dimensional algebraic algebras (when charF = 0). Based on these results, we define a new invariant of an algebra: the Rota–Baxter λ-index rbλ(A)ofanalgebraA as the infimum of the degrees of minimal polynomials of all Rota–Baxter operators of weight λ on A.Wecompute the Rota–Baxter λ-index for the matrix algebra Mn(F), charF =0: it is shown that rbλ(Mn(F)) = 2n−1.
Библиографическая ссылка:
Gubarev V.
Spectrum of Rota - Baxter Operators
International Journal of Algebra and Computation. 2025. P.1-26. DOI: 10.1142/s0218196725500195 WOS Scopus OpenAlex
Spectrum of Rota - Baxter Operators
International Journal of Algebra and Computation. 2025. P.1-26. DOI: 10.1142/s0218196725500195 WOS Scopus OpenAlex
Даты:
| Поступила в редакцию: | 13 авг. 2024 г. |
| Принята к публикации: | 23 апр. 2025 г. |
| Опубликована online: | 6 июн. 2025 г. |
Идентификаторы БД:
| Web of science: | WOS:001503610900001 |
| Scopus: | 2-s2.0-105007533210 |
| OpenAlex: | W3034093496 |
Цитирование в БД:
| БД | Цитирований |
|---|---|
| OpenAlex | 3 |