Indecomposable modules of the intermediate series over W(a,b)  

作　　者：SU YuCai XU Ying YUE XiaoQing 

机构地区：[1]Department of Mathematics,Tongji University [2]Department of Mathematics,Hefei University of Technology

出　　处：《Science China Mathematics》2014年第2期275-291,共17页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11371287,11301130,11001200 and 11101269);the Fundamental Research Funds for the Central Universities Shanghai Municipal Science and Technology Commission(Grant No.12XD1405000)

摘　　要：For any complex parameters a and b,W(a,b)is the Lie algebra with basis{Li,Wi|i∈Z}and relations[Li,Lj]=(j i)Li+j,[Li,Wj]=(a+j+bi)Wi+j,[Wi,Wj]=0.In this paper,indecomposable modules of the intermediate series over W(a,b)are classified.It is also proved that an irreducible Harish-Chandra W(a,b)-module is either a highest/lowest weight module or a uniformly bounded module.Furthermore,if a∈/Q,an irreducible weight W(a,b)-module is simply a Vir-module with trivial actions of Wk’s.For any complex parameters a and b,W（a,b）is the Lie algebra with basis{Li,Wi｜i∈Z}and relations[Li,Lj]=（j i）Li＋j,[Li,Wj]=（a＋j＋bi）Wi＋j,[Wi,Wj]=0.In this paper,indecomposable modules of the intermediate series over W（a,b）are classified.It is also proved that an irreducible Harish-Chandra W（a,b）-module is either a highest/lowest weight module or a uniformly bounded module.Furthermore,if a∈/Q,an irreducible weight W（a,b）-module is simply a Vir-module with trivial actions of Wk’s.

关 键 词：the algebra W（a b） the Virasoro algebra modules of the intermediate series 

分 类 号：O152.5[理学—数学]