三维莱布尼茨代数的导子代数：完整描述

中文摘要 AI 辅助

导子代数是莱布尼茨代数的自然结构不变量。在先前的一系列论文中，已经对若干类单生成、幂零、非幂零以及低维莱布尼茨代数的导子进行了描述。在本文中，我们完成了对任意域上三维非李左莱布尼茨代数的描述。我们利用三维分类的精细化组织，将其分为十六个同构类型，包括带参数的族。先前已知的情形通过引用纳入，并在必要时记录基变换。对于其余情形，我们通过直接系数计算确定导子。特别关注特征为2的情形，此时若干导子代数的维数增加。我们还记录了所得李代数分解为自然理想和子代数的简单分解。最后的表格给出了分类中每一类型的导子代数。

英文摘要

Derivation algebras are natural structural invariants of Leibniz algebras. In a number of earlier papers, derivations were described for several classes of one-generated, nilpotent, non-nilpotent, and low-dimensional Leibniz algebras. In the present paper we complete the description 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 incorporated by reference, with changes of basis recorded when necessary. For the remaining cases we determine the derivations by direct coefficient calculations. Special attention is paid to characteristic two, where several derivation algebras increase in dimension. We also record simple decompositions of the resulting Lie algebras into natural ideals and subalgebras. A final table gives the derivation algebra of every type in the classification.

发表机构

• Oles Honchar Dnipro National University（奥列斯·洪恰尔第聂伯罗国立大学）
• State Tax University（国立税务大学）

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