On split Leibniz algebras (Q765175)

It is well known that the Leibniz algebras theory is a generalisation of the Lie algebras theory; because of this, it is common to move all the concepts and results from the original theory to the new theory to check whether they work properly or not. In this paper, the authors introduce the concept of split Leibniz algebra as a generalisation of the concept of split Lie algebra. Moreover, a new decomposition for this kind of algebras is given. This decomposition is obtained through connections of roots techniques. The last section of this paper studies the case of split Leibniz algebras of maximal length, in order to provide a characterisation of a subclass of the simple Leibniz algebras class. This goal is obtained again through connections of roots techniques.