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

Abstract

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 ⩾ 2 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.