On Derivations of Some Classes of Leibniz Algebras

Abstract

In this paper, we describe the derivations of complex n-dimensional naturally graded filiform Leibniz algebras NGF1, NGF2, and NGF3.We show that the dimension of the derivation algebras of NGF1 and NGF2 equals n+1 and n+2, respectively, while the dimension of the derivation algebra of NGF3 is equal to 2n−1. The second part of the paper deals with the description of the derivations of complex n-dimensional filiform non Lie Leibniz algebras, obtained from naturally graded non Lie filiform Leibniz algebras. It is well known that this class is split into two classes denoted by FLbn and SLbn. Here we found that for L ∈ FLbn, we have n−1≤dimDer(L)≤n+1 and for algebras L from SLbn, the inequality n−1 ≤ dimDer(L) ≤ n+2 holds true.