摘要
Hodge和Parshall在文[On the representation theory of Lie triple systems,Trans AmerMath Soc,2002,354(11):4359-4391]中指出,若(T,(-)^([p]))是有限维限制李三系且(-)^([p]):T→T是单射,则T是可交换的.但是,这个结论是不正确的.作者证明了它在代数闭域上是成立的,同时,给出了限制李三系可交换的一些条件,并刻画了限制李三系的p-映射和半单元的一些性质.
Hodge and Parshall[On the representation theory of Lie triple systems,Trans Amer Math Soc,2002,354（11）：4359-4391]claimed that if T is a finite-dimensional,restricted Lie triple system over K such that（—）^（[p]）：T→T is injective,then T is Abelian.Unfortunately, this conclusion does not hold true.In this paper,the authors prove that the result is valid over an algebraically closed field,and give some conditions for the commutativity of restricted Lie triple systems and characterize some properties of p-mapping and semisimple elements.
出处
《数学年刊（A辑）》
CSCD
北大核心
2010年第3期275-282,共8页
Chinese Annals of Mathematics
基金
国家自然科学基金(No.10701019
No.10871057)
黑龙江省教育厅科学技术研究基金(No.11541366)资助的项目
关键词
限制李三系
P-映射
半单的
P-幂零
Restricted Lie triple systems
p-mapping
Semisimple
p-nilpotent
