Leibniz algebras of dimension 3 over finite fields

TitleLeibniz algebras of dimension 3 over finite fields
Publication TypeJournal Article
Year of Publication2018
AuthorsYashchuk, VS
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2018.07.020
Issue7
SectionMathematics
Pagination20-25
Date Published7/2018
LanguageEnglish
Abstract

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.
Keywordsfactor-algebra, ideal, Leibniz algebra, nilpotent Leibniz algebra
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