On Pre-Novikov Algebras and Derived Zinbiel Variety Научная публикация
| Журнал |
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
ISSN: 1815-0659 |
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| Вых. Данные | Год: 2024, Том: 20, Номер статьи : 017, Страниц : 15 DOI: 10.3842/sigma.2024.017 | ||||||||
| Ключевые слова | Novikov algebra; derivation; dendriform algebra; Zinbiel algebra | ||||||||
| Авторы |
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| Организации |
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Информация о финансировании (1)
| 1 | Институт математики им. С.Л. Соболева СО РАН | FWNF-2022-0002 |
Реферат:
For a non-associative algebra A with a derivation d, its derived algebra A(d) is the same space equipped with new operations a ≻ b = d(a)b, a ≺ b = ad(b), a,b ∈ A. Given a variety Var of algebras, its derived variety is generated by all derived algebras A(d) for all A in Var and for all derivations d of A. The same terminology is applied to binary operads governing varieties of non-associative algebras. For example, the operad of Novikov algebras is the derived one for the operad of (associative) commutative algebras. We state a sufficient condition for every algebra from a derived variety to be embeddable into an appropriate differential algebra of the corresponding variety. We also find that for Var = Zinb, the variety of Zinbiel algebras, there exist algebras from the derived variety (which coincides with the class of pre-Novikov algebras) that cannot be embedded into a Zinbiel algebra with a derivation.
Библиографическая ссылка:
Kolesnikov P.
, Mashurov F.
, Sartayev B.
On Pre-Novikov Algebras and Derived Zinbiel Variety
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2024. V.20. 017 :1-15. DOI: 10.3842/sigma.2024.017 WOS Scopus РИНЦ OpenAlex
On Pre-Novikov Algebras and Derived Zinbiel Variety
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2024. V.20. 017 :1-15. DOI: 10.3842/sigma.2024.017 WOS Scopus РИНЦ OpenAlex
Даты:
| Поступила в редакцию: | 31 авг. 2023 г. |
| Опубликована online: | 28 февр. 2024 г. |
| Опубликована в печати: | 1 апр. 2024 г. |
Идентификаторы БД:
| Web of science: | WOS:001177272600001 |
| Scopus: | 2-s2.0-85186423629 |
| РИНЦ: | 66209073 |
| OpenAlex: | W4392238341 |