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

摘要

This paper is the second in a series of three, the aim of which is toconstruct algebraic geometry over a free metabelian Lie algebra $F$. For theuniversal closure of free metabelian Lie algebra of finite rank $r \ge 2$ overa finite field $k$ we find a convenient set of axioms in the language of Liealgebras $L$ and the language $L_{F}$ enriched by constants from $F$. We give adescription 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 respectivecoordinate algebras. We also prove that the universal theory of a free metabelian Lie algebra overa finite field is decidable in both languages.