FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1996, VOLUME 2, NUMBER 1, PAGES 125-131

On perfect finite-dimensional Lie algebras, satisfying standard Lie identity of degree 5

K. A. Zubrilin
A. Yu. Stepanov

Abstract

View as HTML     View as gif image

Finite-dimensional Lie algebras satisfying standard Lie identity of degree 5 are considered. A base field $K$ is algebraically closed and of zero characteristic. It is shown that any such algebra can be decomposed into a direct sum of a soluble algebra and a perfect one. It is proved that any such perfect algebra is isomorphic to $A$Ä_K sl₂, for a certain commutative and associative $K$-algebra $A$ with unit element, and, thus, satisfies the same identities as Lie algebra $sl$₂.

Location: http://mech.math.msu.su/~fpm/eng/96/961/96105h.htm
Last modified: March 19, 2005