Rota—Baxter operators on the simple Jordan algebra of matrices of order two | Sciact - Система учета научной деятельности ИМ СО РАН

Rota—Baxter operators on the simple Jordan algebra of matrices of order two Научная публикация

Журнал

Bulletin of the Malaysian Mathematical Sciences Society
ISSN: 0126-6705 , E-ISSN: 2180-4206

Вых. Данные

Год: 2025, Том: 48, Номер статьи : 147, Страниц : 12 DOI: 10.1007/s40840-025-01932-3

Ключевые слова

Rota—Baxter operator, matrix algebra, Jordan algebra

Авторы

Gubarev Vsevolod ^1,2 , Panasenko Alexander ^1,2

Организации

1	Novosibirsk State University
2	Sobolev Institute of Mathematics

Информация о финансировании (1)

Российский научный фонд

23-71-10005

We describe all Rota—Baxter operators of any weight on the space of matrices from M2(F) considered under the product a ◦ b = (ab + ba)/2 and usually denoted as M2(F)(+). This algebra is known to be a simple Jordan one. We introduce symmetrized Rota—Baxter operators of weight λ and show that every Rota—Baxter operator of weight 0 on M2(F)(+) either is a Rota—Baxter operator of weight 0 on M2(F) or is a symmetrized Rota—Baxter operator of weight 0 on the same M2(F). We also prove that every Rota—Baxter operator of nonzero weight λ on M2(F)(+) is either a Rota— Baxter operator of weight λ on M2(F) or is, up to the action of φ : R → −R − λid, a symmetrized Rota—Baxter operator of weight λ on M2(F).

Gubarev V. , Panasenko A.
Rota—Baxter operators on the simple Jordan algebra of matrices of order two
Bulletin of the Malaysian Mathematical Sciences Society. 2025. V.48. 147 :1-12. DOI: 10.1007/s40840-025-01932-3 WOS Scopus

Поступила в редакцию:	20 февр. 2025 г.
Принята к публикации:	8 июл. 2025 г.
Опубликована в печати:	17 июл. 2025 г.
Опубликована online:	17 июл. 2025 г.

Web of science:	WOS:001530748000002
Scopus:	2-s2.0-105011051466

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