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

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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 ≥ 2 over a finite field k we find a convenient set of axioms in the language of Lie algebras L and the language LF enriched by constants from F. We give a description of: * The structure of finitely generated algebras from the universal closure of Fᵣ in both L and LFᵣ * The structure of irreducible algebraic sets over Fᵣ 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.