FPM 2003, vol. 9, no. 3, pp. 65-87

FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2003, VOLUME 9, NUMBER 3, PAGES 65-87

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

E. Yu. Daniyarova
I. V. Kazatchkov
V. N. Remeslennikov

Abstract

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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 $r$ ³ 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.

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