单李代数的不可约模上多重线性型空间的研究  

Study of the Space of Multi-linear Forms on Irreducible Modules over Finite Dimensional Simple Lie Algebras

作　　者：刘建岐 王宪栋 LIU Jian-qi;WANG Xian-dong(College of Mathematics and Statistics,Qingdao University,Qingdao 266071,China)

机构地区：[1]青岛大学数学与统计学院

出　　处：《青岛大学学报（自然科学版）》2018年第2期18-22,共5页Journal of Qingdao University(Natural Science Edition)

基　　金：国家自然科学基金(批准号:11472144)资助

摘　　要：研究了复数域上单李代数L的不可约模上多重线性型空间的结构。对三维典型单李代数sl(2,F)的m+1维不可约模V(m),借助于模的张量积方法,讨论了其非零不变多重线性型的存在性。讨论了一般有限维单李代数的情形,得到了两个关于权性质的初步结论。A concrete description of the vector space of multi-linear forms on irreducible modules over finite dimensional Lie algebras on complex field is given.In particular,using the technique of tensor product,the existence of multi-linear forms on V（m）which is the irreducible module of m＋1 dimension over the three dimensional classical simple Lie algebra sl（2,F）are studied.Finally,we got some elementary results about weights by studying the general case.

关 键 词：单李代数 不变多重线性型 不可约模 最高权模 

分 类 号：O152.5[理学—数学]