How to realize a Lie algebra by vector fields

被引：30

作者：

Shchepochkina, I. M. ^{[1
]}

机构：

[1] Independent Univ Moscow, Moscow, Russia

来源：

THEORETICAL AND MATHEMATICAL PHYSICS | 2006年 / 147卷 / 03期

基金：

俄罗斯基础研究基金会;

关键词：

Cartan prolongation; nonintegrable distributions; g(2) structure;

D O I：

10.1007/s11232-006-0078-5

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We describe air algorithm for embedding a finite-dimensional Lie algebra, (superalgebra) into a Lie algebra (superalgebra) of vector fields that is suitable for a ground field of any characteristic and also a way to select the Cartan, complete, and partial prolongations of tire Lie algebra of vector fields using differential equations. We illustrate the algorithm with the example of Cartan's interpretation of the exceptional simple Lie algebra g(2) as the Lie algebra preserving a certain nonintegrable distribution and also several other examples.

引用

页码：821 / 838

页数：18

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