On nilpotent Leibniz \(n\)-algebras (Q2893002)

Leibniz \(n\)-algebras were recently discovered. Leibniz \(n\)-algebra concept is one possible generalization of Lie algebra concept, so there are a lot of solved questions in Lie algebra theory which remain open in Leibniz \(n\)-algebra theory. In this paper, the authors establish the concept of nilpotency, give the Engel's theorem and sufficient conditions to know whether or not an algebra is nilpotent. Furthermore, the classification of the Leibniz 3-algebras of dimension 2 is given.