李代数W[G]的自同构群与Verma模  

Automorphism Group and Verma Module for Lie Algebra W[G]

作　　者：徐崇斌[1,2] 

机构地区：[1]温州大学数学与信息科学学院,浙江温州325035 [2]华南理工大学理学院数学系,广东广州510640

出　　处：《温州大学学报（自然科学版）》2012年第3期13-20,共8页Journal of Wenzhou University(Natural Science Edition)

摘　　要：设F是特征0的域,G是它的加法子群,相应于F和群G,定义一类李代数W[G].在本文里,李代数W[G]的自同构群与Verma模的可约性得到仔细地研究.其中自同构群的确定主要依赖于一些特殊自同构的构造,而Verma模的可约性完全取决于W[G]中元I0的作用是否为零.Let F be a field of characteristic 0,G an additive subgroup of F.Associated to F and G,a class of Lie algebra W[G] could be defined.In this paper,the automorphism group of Lie algebra W[G] and reducibility of Verma module were investigated carefully.Results showed that the determination of automorphism group is based on constructions of some special automorphisms and the reducibility of Verma module depends on whether the action of the element I0is zero.

关 键 词：李代数W[G] 自同构群 VERMA模 

分 类 号：O152.5[理学—数学]