限制李三系的可换性  

The Commutativity of Restricted Lie Triple Systems

作　　者：陈良云[1] 徐晓宁[2] 林洁[3] 

机构地区：[1]东北师范大学数学与统计学院,长春130024 [2]辽宁大学数学学院,沈阳110036 [3]中国民航大学中欧航空工程师学院,天津300300

出　　处：《数学年刊（A辑）》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

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.

关 键 词：限制李三系 P-映射 半单的 P-幂零 

分 类 号：O152.5[理学—数学]