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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.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 3, pp. 65–87, 2003.

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Daniyarova, E.Y., Kazatchkov, I.V. & Remeslennikov, V.N. Algebraic geometry over free metabelian lie algebras. II. Finite-field case. J Math Sci 135, 3311–3326 (2006). https://doi.org/10.1007/s10958-006-0160-4

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Keywords

  • Algebraic Geometry
  • Finite Field
  • Finite Rank
  • Universal Theory
  • Universal Closure