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摘要翻译：
本文是一系列三篇文章中的第一篇，其目的是为自由metabelian李代数奠定代数几何的基础。本文引入了metabelian Lie$u$-代数的概念，建立了metabelian Lie$u$-代数与特殊矩阵李代数之间的联系。定义了元李代数$a$的$\delta$-局部化和拟合根$a$的直模扩张，并证明了这些代数位于$a$的泛闭包中。
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英文标题：
《Algebraic Geometry over Free Metabelian Lie Algebra I: U-Algebras and
Universal Classes》
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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 first in a series of three, the aim of which is to lay the foundations of algebraic geometry over the free metabelian Lie algebra $F$. In the current paper we introduce the notion of a metabelian Lie $U$-algebra and establish connections between metabelian Lie $U$-algebras and special matrix Lie algebras. We define the $\Delta $-localisation of a metabelian Lie $U$-algebra $A$ and the direct module extension of the Fitting's radical of $A$ and show that these algebras lie in the universal closure of $A$.
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PDF链接：
https://arxiv.org/pdf/0710.3871
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