On the derivations of Leibniz algebras of low dimension





dimension, derivation, hypercenter, Leibniz algebra, nilpotent Leibniz algebra


Let L be an algebra over a field F. Then L is called a left Leibniz algebra if its multiplication operations [×, ×] addition- ally satisfy the so-called left Leibniz identity: [[a,b],c] = [a,[b,c]] [b,[a,c]] for all elements a, b, c Î L. In this paper, we begin the description of the algebra of derivations of Leibniz algebras having dimension 3. It is clear that the description of the algebra of derivations of all Leibniz algebras, having dimension 3, is quite large. Therefore, in this article, we will focus on the description of the nilpotent Leibniz algebra, whose nilpotency class is 3, and the nilpotent Leibniz algebra, whose center has dimension 2.


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How to Cite

Kurdachenko, L. ., Semko, M. ., & Yashchuk, V. . (2023). On the derivations of Leibniz algebras of low dimension. Reports of the National Academy of Sciences of Ukraine, (2), 18–23. https://doi.org/10.15407/dopovidi2023.02.018