Restricted Lie algebras all whose elements are semisimple

被引：0

作者：

Chen, Liangyun ^{[2
]}

Xu, Xiaoning ^{[1
]}

Zhang, Yongzheng ^{[2
]}

机构：

[1] Liaoning Univ, Sch Math, Shenyang 110036, Peoples R China

[2] NE Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China

来源：

FRONTIERS OF MATHEMATICS IN CHINA | 2011年 / 6卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Restricted Lie algebra; ad-semisimple; simple-semiabelian; semisimple element; p-simple-semiabelian; TRIPLE-SYSTEMS; SUBALGEBRAS;

D O I：

10.1007/s11464-010-0091-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

People studied the properties and structures of restricted Lie algebras all whose elements are semisimple. It is the main objective of this paper to continue the investigation in order to obtain deeper structure theorems. We obtain some sufficient conditions for the commutativity of restricted Lie algebras, generalize some results of R. Farnsteiner and characterize some properties of a finite-dimensional semisimple restricted Lie algebra all whose elements are semisimple. Moreover, we show that a centralsimple restricted Lie algebra all whose elements are semisimple over a field of characteristic p > 7 is a form of a classical Lie algebra.

引用

页码：61 / 70

页数：10

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