On the commutator in Leibniz algebras
Dzhumadildaev A.S. Ismailov N.A. Sartayev B.K.
1 June 2022World Scientific
International Journal of Algebra and Computation
2022#32Issue 4785 - 805 pp.
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 Dzhumadildaev in [A. S. Dzhumadildaev, 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.
anti-commutator , commutator , computer algebra , Leibniz algebras , polynomial identities
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Kazakh-British Technical Unversity, Almaty, Kazakhstan
Saint Petersburg University, Saint Petersburg, Russian Federation
Astana It University, Nur-Sultan, Kazakhstan
Sobolev Institute of Mathematics, Novosibirsk, Russian Federation
Suleyman Demirel University, Kaskelen, Kazakhstan
Kazakh-British Technical Unversity
Saint Petersburg University
Astana It University
Sobolev Institute of Mathematics
Suleyman Demirel University
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