Algebraic geometry over free metabelian lie algebras. I. U-algebras and universal classes
| Autor: | I. V. Kazatchkov, Vladimir N. Remeslennikov, E. Yu. Daniyarova |
|---|---|
| Rok vydání: | 2006 |
| Předmět: |
Statistics and Probability
Pure mathematics Current (mathematics) Series (mathematics) Applied Mathematics General Mathematics Mathematics::Rings and Algebras Universal closure Mathematics - Logic Extension (predicate logic) Algebraic geometry Mathematics::Geometric Topology Mathematics - Algebraic Geometry Mathematics::Group Theory Matrix (mathematics) Lie algebra FOS: Mathematics Algebra over a field Logic (math.LO) Algebraic Geometry (math.AG) Mathematics |
| Zdroj: | Journal of Mathematical Sciences. 135:3292-3310 |
| ISSN: | 1573-8795 1072-3374 |
| Popis: | This paper is the first in a series of three, the aim 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 Lie $U$-algebra and establish connections between metabelian Lie $U$-algebras and special matrix Lie algebras. We define the $\Delta $-localisation of a metabelian Lie $U$-algebra $A$ and the direct module extension of the Fitting's radical of $A$ and show that these algebras lie in the universal closure of $A$. Comment: 34 pages |
| Databáze: | OpenAIRE |
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