Algebraic geometry over free metabelian Lie algebras. II. Finite-field case

This paper is the second in a series of three, the object of which is to construct an algebraic geometry over the free metabelian Lie algebra $F$. For the universal closure of a free metabelian Lie algebra of finite rank $r\ge2$ over a finite field $k$ we find convenient sets of axioms in two distinct languages: with constants and without them. We give a description of the structure of finitely generated algebras from the universal closure of $F_r$ in both languages mentioned and the structure of irreducible algebraic sets over $F_r $ and respective coordinate algebras. We also prove that the universal theory of free metabelian Lie algebras over a finite field is decidable in both languages.