On the Special Identities of Gelfand–Dorfman Algebras Научная публикация
| Журнал |
Experimental Mathematics
ISSN: 1058-6458 , E-ISSN: 1944-950X |
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| Вых. Данные | Год: 2022, DOI: 10.1080/10586458.2022.2041134 | ||||
| Ключевые слова | Gelfand–Dorfman algebra; Gröbner basis; operad; Poisson algebra; special identity | ||||
| 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:
A Gelfand–Dorfman algebra (GD-algebra) is said to be special if it can be embedded into a differential Poisson algebra. In this paper, we prove that the class of all special GD-algebras is closed with respect to homomorphisms and thus forms a variety. We describe a technique for finding potentially all special identities of GD-algebras and derive two known special identities of degree 4 in this way. By computing the Gröbner basis for the corresponding shuffle operad, we show that these two identities imply all special ones up to degree 5.
Библиографическая ссылка:
Kolesnikov P.S.
, Sartayev B.K.
On the Special Identities of Gelfand–Dorfman Algebras
Experimental Mathematics. 2022. DOI: 10.1080/10586458.2022.2041134 WOS Scopus РИНЦ OpenAlex
On the Special Identities of Gelfand–Dorfman Algebras
Experimental Mathematics. 2022. DOI: 10.1080/10586458.2022.2041134 WOS Scopus РИНЦ OpenAlex
Идентификаторы БД:
| Web of science: | WOS:000771257500001 |
| Scopus: | 2-s2.0-85126741159 |
| РИНЦ: | 48193754 |
| OpenAlex: | W4302395996 |