On the derivations of Leibniz algebras of low dimension - Kurdachenko, L.A.; Semko, M.M.; Yashchuk, V.S. (Доповіді НАН України, 2023)
Let L be an algebra over a field F. Then L is called a left Leibniz algebra if its multiplication operations [⋅, ⋅] additionally satisfy the so-called left Leibniz identity: [[a,b],c] = [a,[b,c]] – [b,[a,c]] for all elements a, b, c ∈ 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.