Algebraic Geometry over Free Metabelian Lie Algebra II: Finite Field Case - Mathematics > Algebraic GeometryReport as inadecuate




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Abstract: This paper is the second in a series of three, the aim of which is toconstruct algebraic geometry over a free metabelian Lie algebra $F$. For theuniversal closure of free metabelian Lie algebra of finite rank $r \ge 2$ overa finite field $k$ we find a convenient set of axioms in the language of Liealgebras $L$ and the language $L {F}$ enriched by constants from $F$. We give adescription of:* The structure of finitely generated algebras from the universal closure of$F r$ in both $L$ and $L {F r}$* The structure of irreducible algebraic sets over $F r $ and respectivecoordinate algebras.We also prove that the universal theory of a free metabelian Lie algebra overa finite field is decidable in both languages.



Author: E. Daniyarova, I. Kazachkov, V. Remeslennikov

Source: https://arxiv.org/







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