Derivations and centroids of finite dimensional dialgebras - Mohamed, Mohamed Abubakar Hagi (2016)
The thesis deals with the derivations, generalized derivations and centroids of associative and diassociative algebras. In all the cases, we give an algorithm to find the derivation algebras. The algorithm is applied to compute the derivations of low dimensional diassociative algebras. Having found the derivations, we determine those diassociative algebras that are characteristically nilpotent. Some basic properties of derivations in terms of left and right multiplication operators are also given for each case. We introduce a generalization of derivation of diassociative algebras and study its properties. The generalization of derivation depends on parameters (a;b; g); we specify all possible values of the parameters. All of the generalized derivations of low-dimensional complex diassociative algebras are given. We also introduce the concept of centroid for associative and diassociative algebras and study some of their properties. An algorithm to find centroids of algebras is given as well. The algorithm is then applied to determine the centroids of low dimensional algebras.