一类无限维Lie代数的不可约模  

Irreducible modules of a class infinite dimensional Lie algebra

作　　者：姚廷富[1] 吴宗显[1] 施妮沙[1] 戴先胜 YAO Tingfu;WU Zongxian;SHI Nisha;DAI Xiansheng(College of Mathematics and Information Science,Guiyang University,Guiyang 550005,China;College of Mathematics Science,Guizhou Normal University,Guiyang 550001,China)

机构地区：[1]贵阳学院数学与信息科学学院,贵州贵阳550005 [2]贵州师范大学数学科学学院,贵州贵阳550001

出　　处：《安徽大学学报（自然科学版）》2018年第4期61-64,共4页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11761016);贵州省科学技术基金资助项目(黔科合J字LKG[2013]31;黔科合J字LKG[2013]30;黔科合J字LKG[2013]28);贵阳学院信息与计算科学专业综合改革项目(20140465105)

摘　　要：研究无限维Lie代数的结构和表示是Lie代数的主要课题,无限维Lie代数的不可约模是具体的一类表示.采用构造法给出了一类无限维Lie代数G的忠实模,同时给出此模为不可约模的一个充要条件,然后用反证法与基元素检验法证明该结果.此结果对研究无限维Lie代数的性质与表示有一定意义.h was main topic of infinite dimensional Lie algebras that studied the structures and representations. Irreducible modules of an infinite dimensional Lie algebra were one of the concrete representations. Here structured approaches were used to give the faithful modules of a class infinite dimensional Lie algebra. Meanwhile, it gave a necessary and sufficient condition of irreducible modules for the faithful modules, afterwards, it took proofs by contradictions and testing the base elements to verify the results. This result indicated that it had great significance in researching the property and representation of infinite dimensional Lie algebras.

关 键 词：无限维Lie代数 忠实模 不可约模 

分 类 号：O156[理学—数学]