Geodesic
Algebraic geometry over free metabelian Lie algebras. I. U-algebras and universal classes
Fundamentalʹnaâ i prikladnaâ matematika, Tome 9 (2003) no. 3, pp. 37-63 
E. Yu. Daniyarova; I. V. Kazatchkov; V. N. Remeslennikov. Algebraic geometry over free metabelian Lie algebras. I. U-algebras and universal classes. Fundamentalʹnaâ i prikladnaâ matematika, Tome 9 (2003) no. 3, pp. 37-63. http://geodesic.mathdoc.fr/item/FPM_2003_9_3_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

This paper is the first in a series of three, the object of which is to lay the foundations of algebraic geometry over the free metabelian Lie algebra $F$. In the current paper, we introduce the notion of a metabelian U-Lie algebra and establish connections between metabelian U-Lie algebras and special matrix Lie algebras. We define the $\Delta$-localization of a metabelian U-Lie algebra $A$ and the direct module extension of the Fitting radical of $A$ and show that these algebras lie in the universal closure of $A$.

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