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素特征李代数概述
引用本文:林磊.素特征李代数概述[J].数学进展,1995,24(1):28-38.
作者姓名:林磊
作者单位:华东师范大学数学系
摘    要:近20年来,国内外在素特征李代数的研究中取得了许多突破性的进展,本文是近年来国内外在这一领域的研究成果的一个综述,第一部分对Cartan型李代数的定义以及主要结构的回顾,然后,重点介绍了两个重的分类定理,即,素特征域上的有限维局限单李代数的分类定理以及素特征域上的有际维单李代的分类定理。由于后一分类是一前一分类的基础上完成的,所以,本文对第一个分类定理的证明作了一个简单的介绍,在第三部分中,对素特

关 键 词:素特征李代数  Cartan型  表示论  李代数

A Survey on Lie Algebra of Prime Characteristic
Lin Lei.A Survey on Lie Algebra of Prime Characteristic[J].Advances in Mathematics,1995,24(1):28-38.
Authors:Lin Lei
Abstract:During recent twenty years,in the study of Lie algebra of primecharacteristic,a lot of outstanding advances have been obtained.This survey paperconcerns with major achievements.It is essential (1)to recall definitions and struc-tures of Lie algebras of Cartan type;(2)to introduce emphatically the two importantclassification theorems:the one of finite dimensional restricted Lie algebras and theother of non-restricted ones;(3)to make a survey of the results on the representa_tion theory of Lie algebras,especially,on the graded representation theory of gradedLie algebras. In addition,since both the classification theorems do not concern withLie algebras of small characteristic,achievements on the constructions of simple Liealgebras of small characteristic are reviewed.
Keywords:Lie algebra of prime characteristic  Cartan type  representationtheory  small characteristics
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