FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2003, VOLUME 9, NUMBER 3, PAGES 37-63

Algebraic geometry over free metabelian Lie algebras. I. U-algebras and universal classes

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

Abstract

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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 $$D-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 $A$.

Location: http://mech.math.msu.su/~fpm/eng/k03/k033/k03304h.htm.
Last modified: January 24, 2005.