Leibniz algebras of dimension 3 over finite fields - Yashchuk, V.S. (Reports of the National Academy of Sciences of Ukraine, 2018)
The first thing in the study of all types of algebras is the description of algebras having small dimensions. Unlike the simpler cases of 1- and 2-dimensional Leibniz algebras, the structure of 3-dimensional Leibniz algebras is more complicated. We consider the structure of Leibniz algebras of dimension 3 over a finite field. In some cases, the structure of the algebra essentially depends on the characteristic of the field. In others, it depends on the solvability of specific equations in the field, and so on.