On some Leibniz algebras having small dimension

The first step in the study of all types of algebras is the description of such algebras having small dimensions. The structure of 3-dimensional Leibniz algebras is more complicated than 1- and 2-dimensional cases. In this paper, we consider the structure of Leibniz algebras of dimension 3 over the finite fields. In some cases, the structure of the algebra essentially depends on the characteristic of the field, in others on the solvability of specific equations in the field, and so on.