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arXiv · 0710.3872

Algebraic Geometry over Free Metabelian Lie Algebra II: Finite Field Case

E. Daniyarova·I. Kazachkov·V. Remeslennikov
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Abstract

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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E. Daniyarova, I. Kazachkov, V. Remeslennikov. 2007-10-20. Algebraic Geometry over Free Metabelian Lie Algebra II: Finite Field Case. https://doi.org/10.1007/s10958-006-0160-4

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