On some non-nilpotent Leibniz algebras of dimension 3 and their automorphism groups

• Date: 2026
• Author Affiliations: Leonid A. Kurdachenko; Oleksandr O. Pypka — Oles Honchar Dnipro National University; Igor Ya. Subbotin
• Keywords: keywords
• Main Authors: Kurdachenko, Leonid A., Pypka, Oleksandr O., Subbotin, Igor Ya.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2026
• Subjects: Leibniz algebra; automorphism group; Leibniz kernel; center; 17A32; 17A36
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2499
• Journal Title: Algebra and Discrete Mathematics

Let \(L\) be an algebra over a field \(F\) with the binary operations \(+\) and \([,]\). Then \(L\) is called a (left) Leibniz algebra if it satisfies the (left) Leibniz identity: \([a,[b,c]]=[[a,b],c]+[b,[a,c]]\) for all \(a,b,c\in L\). A linear transformation \(f\) of \(L\) is called an endomorphism of \(L\) if \(f([a,b])=[f(a),f(b)]\) for all \(a,b\in L\). A bijective endomorphism of \(L\) is called an automorphism of \(L\). The main goal of this article is to describe the structure of automorphism groups of certain types of non-nilpotent three-dimensional Leibniz algebras over an arbitrary field \(F\).