In this paper we introduce the concept of centroid and derivation of Leibniz algebras. By using the classification results of Leibniz algebras obtained earlier, we describe the centroids and derivations of low-dimensional Leibniz algebras. We also study some properties of centroids of Leibniz algebras and use these properties to categorize the algebras to have socalled small centroids. The description of the derivations enables us to specify an important subclass of Leibniz algebras called characteristically nilpotent.
In this paper we investigated the concept of generalized derivations of finite dimensional algebras and their properties. The definition of the generalized derivation depends on some parameters and in particular on values of the parameters, we obtain classical concept of derivation and its generalizations. We use an algorithm for calculating the generalized derivations of Lie and Leibniz algebras.
This paper's central theme is to prove the existence of an n-algebra whose multiplication cannot be expressed employing any binary operation. Furthermore, to prove if two algebras are not isomorphic, this property does not hold for 3-algebras corresponding to these two algebras. The proof drives applying some results gotten early applying a new approach for the classification algebras problem, introduced recently, which showed great success in solving many classification algebras problems.
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