Irreducible A1（1）-modules from modules over two-dimensional non-abelian Lie algebra  

作　　者：Genqiang LIU Yueqiang ZHAO 

机构地区：[1]School of Mathematics and Statistics, Henan University, Kaifeng 475004, China

出　　处：《Frontiers of Mathematics in China》2016年第2期353-363,共11页中国高等学校学术文摘·数学（英文）

基　　金：The authors would like to thank the referees for nice suggestions. This work was supported in part by the National Natural Science Foundation of China （Grant No. 11301143） and the school fund of Henan University （yqpy20140044）.

摘　　要：For any module V over the two-dimensional non-abelian Lie algebra b and scalar a ∈C, we define a class of weight modules Fα（V） with zero central charge over the affine Lie algebra A（1）. These weight modules have infinite- dimensional weight spaces if and only if V is infinite dimensional. In this paper, we will determine necessary and sufficient conditions for these modules Fα（V） to be irreducible. In this way, we obtain a lot of irreducible weight A1（1）-modules with infinite-dimensional weight spaces.For any module V over the two-dimensional non-abelian Lie algebra b and scalar a ∈C, we define a class of weight modules Fα（V） with zero central charge over the affine Lie algebra A（1）. These weight modules have infinite- dimensional weight spaces if and only if V is infinite dimensional. In this paper, we will determine necessary and sufficient conditions for these modules Fα（V） to be irreducible. In this way, we obtain a lot of irreducible weight A1（1）-modules with infinite-dimensional weight spaces.

关 键 词：Atone Lie algebras irreducible modules weight modules 

分 类 号：O152.5[理学—数学] TP311[理学—基础数学]