自由亚阿贝尔李代数II上的Algebraic Geometry：有限域情形
Algebraic Geometry over Free Metabelian Lie Algebra II: Finite Field Case
摘要：
本文是第二系列的三个，其目的是建立代数几何上的自由亚交换李代数$F$。对于有限域$k$上有限秩$r \ge 2$的自由亚交换李代数的泛闭包，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.我们给出一个描述：* 在$L$和$L_{F_r}$中由$F_r$的泛闭包生成的代数的结构 * 在$F_r $和相应的坐标代数上的不可约代数集的结构。我们还证明了有限域上自由亚阿贝尔李代数的泛理论在两种语言中都是可判定的。
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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