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

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

2007-10-20

arxiv.org/abs/0710.3872v1

Journal of Mathematical Sciences, Volume 135, Number 5 / June, 2006, p. 3311-3326

Mathematics

Algebraic Geometry

31 pages

Scientific paper

10.1007/s10958-006-0160-4

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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