Algebraic Geometry over Free Metabelian Lie Algebra I: U-Algebras and Universal Classes

Details Algebraic Geometry over Free Metabelian Lie Algebra I: U-Algebras and Universal Classes Algebraic Geometry over Free Metabelian Lie Algebra I: U-Algebras and Universal Classes

2007-10-20

arxiv.org/abs/0710.3871v1

Journal of Mathematical Sciences, Volume 135, Number 5 / June, 2006, p 3292-3310

Mathematics

Algebraic Geometry

34 pages

Scientific paper

10.1007/s10958-006-0159-x

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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