发表机构
Oles Honchar Dnipro National University; State Tax University（奥列斯·洪恰尔第聂伯国立大学; 国家税务大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文完整描述了任意域上三维非李左莱布尼兹代数的自同构群，基于十六类精细分类，通过直接分析自同构条件确定各类型群，并特别处理例外参数与特征二情形。
AI 中文摘要
自同构群是代数最自然的结构不变量之一，其显式确定是莱布尼兹代数结构理论中的一个基本问题。在先前的一系列论文中，已获得了若干类低维、单生成、幂零和非幂零莱布尼兹代数的自同构群。在本文中，我们完成了对任意域上三维非李左莱布尼兹代数这一图景的补全。我们使用三维分类的精细组织，将其分为十六个同构类型，包括参数化族。先前已知的情形不重新计算，而是通过引用纳入，并在必要时记录基变换。对于其余类型，我们通过直接分析自同构条件来显式确定自同构群。特别关注例外参数值和特征二的情形。最后的表格总结了分类中每个类型的自同构群。
英文摘要
Automorphism groups are among the most natural structural invariants of an algebra, and their explicit determination is a basic problem in the structure theory of Leibniz algebras. In a series of earlier papers, automorphism groups were obtained for several classes of low-dimensional, one-generated, nilpotent, and non-nilpotent Leibniz algebras. In the present paper we complete this picture for three-dimensional non-Lie left Leibniz algebras over arbitrary fields. We use a refined organization of the three-dimensional classification into sixteen isomorphism types, including parameterized families. Previously known cases are not recomputed; instead, they are incorporated by reference, with changes of basis recorded when necessary. For the remaining types we determine the automorphism groups explicitly through a direct analysis of the automorphism conditions. Particular attention is paid to exceptional parameter values and to characteristic two. A final table summarizes the automorphism group of every type in the classification.
