On split Lie triple systems II

被引：0
作者：
Antonio J. Calderón Martín
M. Forero Piulestán
机构：
[1] Universidad de Cádiz,Departamento de Matemáticas
来源：
Proceedings - Mathematical Sciences | 2010年 / 120卷
关键词：
Lie triple system; system of roots; root space; split Lie algebra; structure theory;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In [4] it is studied that the structure of split Lie triple systems with a coherent 0-root space, that is, satisfying [T0, T0, T] = 0 and [T0, Tα, T0] ≠ 0 for any nonzero root α and where T0 denotes the 0-root space and Tα the α-root space, by showing that any of such triple systems T with a symmetric root system is of the form T = U + ΣjIj with U 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. It is also shown in [4] that under certain conditions, a split Lie triple system with a coherent 0-root space 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. In the present paper we extend these results to arbitrary split Lie triple systems with no restrictions on their 0-root spaces.
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页码：185 / 198
页数：13
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