On split Lie triple systems

被引：0

作者：

Calderón Martín A.J. ^{[1
]}

机构：

[1] Departamento de Matemáticas, Universidad de Cádiz, Cádiz

来源：

Proceedings - Mathematical Sciences | 2009年 / 119卷 / 2期

关键词：

Lie triple system; Root space; Split Lie algebra; Structure theory; System of roots;

D O I：

10.1007/s12044-009-0017-0

中图分类号：

学科分类号：

摘要：

We begin the study of arbitrary split Lie triple systems by focussing on those with a coherent 0-root space. We show that any such triple systems T with a symmetric root system is of the form T = U{script} + Σj Ij with U{script} a subspace of the 0-root space T0 and any Ij a well described ideal of T, satisfying [Ij, T, Ik] = 0 if j ≠ k. Under certain conditions, it is shown that T is the direct sum of the family of its minimal ideals, each one being a simple split Lie triple system, and the simplicity of T is characterized. The key tool in this job is the notion of connection of roots in the framework of split Lie triple systems. © Printed in India.

引用

页码：165 / 177

页数：12

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