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摘要翻译：
本文研究有限维复非李丝状莱布尼兹代数的分类问题。实际上，观察表明，得到丝状莱布尼兹代数分类的资源有两个。第一个是自然分次的无李丝状Leibniz代数，另一个是自然分次的丝状李代数。利用第一个资源，我们得到了两个不相交的filiform Leibniz代数类。本文讨论了上述两类中的第二类，第一类在我们以前的论文中已经考虑过。这里的代数分类是指指定轨道的代表，而几何分类是在代数几何意义上寻找一般结构常数的问题。我们在这篇论文中的主要工作是代数分类。我们在这里提出了一种基于不变量的代数方法。利用该方法，对于任意给定的低维情形，可以对所有的丝状Leibniz代数进行分类。此外，所得结果可用于此类代数轨道的几何分类。
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英文标题：
《On Classification of Finite Dimensional Complex Filiform Leibniz
Algebras (Part 2)》
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作者：
U. D. Bekbaev, I. S. Rakhimov
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Rings and Algebras 环与代数
分类描述：Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups
非交换环与代数，非结合代数，泛代数与格论，线性代数，半群
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
The paper is devoted to classification problem of finite dimensional complex none Lie filiform Leibniz algebras. Actually, the observations show there are two resources to get classification of filiform Leibniz algebras. The first of them is naturally graded none Lie filiform Leibniz algebras and the another one is naturally graded filiform Lie algebras. Using the first resource we get two disjoint classes of filiform Leibniz algebras. The present paper deals with the second of the above two classes, the first class has been considered in our previous paper. The algebraic classification here means to specify the representatives of the orbits, whereas the geometric classification is the problem of finding generic structural constants in the sense of algebraic geometry. Our main effort in this paper is the algebraic classification. We suggest here an algebraic method based on invariants. Utilizing this method for any given low dimensional case all filiform Leibniz algebras can be classified. Moreover, the results can be used for geometric classification of orbits of such algebras.
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PDF链接：
https://arxiv.org/pdf/0704.3885
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