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On the commutator in Leibniz algebras Научная публикация

Журнал

International Journal of Algebra and Computation
ISSN: 0218-1967 , E-ISSN: 1793-6500

Вых. Данные

Год: 2022, Том: 32, Номер: 4, Страницы: 785-805 Страниц : 21 DOI: 10.1142/S0218196722500333

Ключевые слова

anti-commutator; commutator; computer algebra; Leibniz algebras; polynomial identities

Авторы

Dzhumadil'daev A.S. ^1,2 , Ismailov N.A. ^2,3 , Sartayev B.K. ^4,5

Организации

1	Kazakh-British Technical Unversity, Almaty, Kazakhstan
2	Saint Petersburg University, Saint Petersburg, Russian Federation
3	Astana It University, Nur-Sultan, Kazakhstan
4	Sobolev Institute of Mathematics, Novosibirsk, Russian Federation
5	Suleyman Demirel University, Kaskelen, Kazakhstan

We prove that the class of algebras embeddable into Leibniz algebras with respect to the commutator product is not a variety. It is shown that every commutative metabelain algebra is embeddable into Leibniz algebras with respect to the anti-commutator. Furthermore, we study polynomial identities satisfied by the commutator in every Leibniz algebra. We extend the result of Dzhumadil'daev in [A. S. Dzhumadil'daev, q-Leibniz algebras, Serdica Math. J. 34(2) (2008) 415-440]. to identities up to degree 7 and give a conjecture on identities of higher degrees. As a consequence, we obtain an example of a non-Spechtian variety of anticommutative algebras.

Dzhumadil'daev A.S. , Ismailov N.A. , Sartayev B.K.
On the commutator in Leibniz algebras
International Journal of Algebra and Computation. 2022. V.32. N4. P.785-805. DOI: 10.1142/S0218196722500333 WOS Scopus РИНЦ OpenAlex

Поступила в редакцию:	12 авг. 2021 г.
Принята к публикации:	18 янв. 2022 г.
Опубликована online:	21 февр. 2022 г.
Опубликована в печати:	5 апр. 2022 г.

Web of science:	WOS:000806970600006
Scopus:	2-s2.0-85125532494
РИНЦ:	48187804
OpenAlex:	W4213389302

БД	Цитирований
Scopus	2
Web of science	1
OpenAlex	2