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摘要翻译：
研究了低维复非李丝状Leibniz代数的分类问题。得到丝状莱布尼兹代数的分类有两个来源。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。这里我们确实考虑了从自然分次的无李丝状莱布尼兹代数中出现的莱布尼兹代数。这个类可以分成两个子类。然而，没有研究每个类内的同构。在U.D.Bekbaev和I.S.Rakhimov之前，提出了用不变量来解决同构问题的方法。本文给出了它们的结果在低维情况下的实现。本文从上述结果的第一类出发，给出维数至多为8的复非李丝状Leibniz代数的完全分类，并给出有限维情形下同构类个数的假设公式。
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英文标题：
《On Isomorphism Classes and Invariants of Low Dimensional Complex
Filiform Leibniz Algebras (PART 1)》
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作者：
I.S. Rakhimov, S.K. Said Husain
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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 aims to investigate the classification problem of low dimensional complex none Lie filiform Leibniz algebras. There are two sources to get classification of filiform Leibniz algebras. The first of them is the naturally graded none Lie filiform Leibniz algebras and the another one is the naturally graded filiform Lie algebras. Here we do consider Leibniz algebras appearing from the naturally graded none Lie filiform Leibniz algebras. This class can be splited into two subclasses. However, isomorphisms within each class there were not investigated. Before U.D.Bekbaev and I.S.Rakhimov suggested an approach to the isomorphism problem in terms of invariants. This paper presents an implementation of their result in low dimensional cases. Here we give the complete classification of complex none Lie filiform Leibniz algebras in dimensions at most 8 from the first class of the above mentioned result and give a hypothetic formula for the number of isomorphism classes in finite dimensional case.
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PDF链接：
https://arxiv.org/pdf/0710.0121
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