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摘要翻译：
本文是三个系列中的第二个，其目的是在一个自由的metabelian李代数上构造代数几何。对于有限域$K$上有限秩的自由元贝尔李代数$R\ge2$的泛闭包，我们在李代数语言$L$和由$F$中的常数丰富的语言$L_{F}$中找到了一组方便的公理。我们给出了在$L$和$L_{F_r}中由$F_r$的泛闭包得到的有限生成代数的结构，$F_r$上的不可约代数集的结构和相应的坐标代数。我们还证明了有限域上自由metabelian李代数的泛理论在两种语言中都是可判定的。
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英文标题：
《Algebraic Geometry over Free Metabelian Lie Algebra II: Finite Field
Case》
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作者：
E. Daniyarova, I. Kazachkov, V. Remeslennikov
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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：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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一级分类：Mathematics 数学
二级分类：Logic 逻辑
分类描述：Logic, set theory, point-set topology, formal mathematics
逻辑，集合论，点集拓扑，形式数学
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英文摘要：
This paper is the second in a series of three, the aim of which is to construct algebraic geometry over a free metabelian Lie algebra $F$. For the universal closure of free metabelian Lie algebra of finite rank $r \ge 2$ over a finite field $k$ we find a convenient set of axioms in the language of Lie algebras $L$ and the language $L_{F}$ enriched by constants from $F$. We give a description of: * The structure of finitely generated algebras from the universal closure of $F_r$ in both $L$ and $L_{F_r}$ * The structure of irreducible algebraic sets over $F_r $ and respective coordinate algebras. We also prove that the universal theory of a free metabelian Lie algebra over a finite field is decidable in both languages.
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PDF链接：
https://arxiv.org/pdf/0710.3872
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