On split Lie algebras with symmetric root systems

被引：47

作者：

Calderon Martin, Antonio J. ^{[1
]}

机构：

[1] Univ Cadiz, Dept Matemat, Cadiz 11510, Spain

来源：

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES | 2008年 / 118卷 / 03期

关键词：

infinite dimensional Lie algebras; split Lie algebras; roots;

D O I：

10.1007/s12044-008-0027-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We develop techniques of connections of roots for split Lie algebras with symmetric root systems. We show that any of such algebras L is of the form L = u + Sigma(j) I-j with u a subspace of the abelian Lie algebra H and any I-j a well described ideal of L, satisfying [I-j, I-k] = 0 if j not equal k. Under certain conditions, the simplicity of L is characterized and it is shown that L is the direct sum of the family of its minimal ideals, each one being a simple split Lie algebra with a symmetric root system and having all its nonzero roots connected.

引用

页码：351 / 356

页数：6