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

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.

31 pages

Cited by in corpus (1)

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