On the commutator in Leibniz algebras

On the commutator in Leibniz algebras Full article

Journal

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

Output data

Year: 2022, Volume: 32, Number: 4, Pages: 785-805 Pages count : 21 DOI: 10.1142/S0218196722500333

Tags

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

Authors

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

Affiliations

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

Submitted:	Aug 12, 2021
Accepted:	Jan 18, 2022
Published online:	Feb 21, 2022
Published print:	Apr 5, 2022

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

DB	Citing
Scopus	2
Web of science	1
OpenAlex	2