Classification of Irreducible Weight Modules with a Finite-dimensional Weight Space over Twisted Heisenberg-Virasoro Algebra  

作　　者：Ran SHEN Yu Cai SU 

机构地区：[1]Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, P. R. China [2]College of Science, Donghua University, Shanghai 201600, P. R. China [3]Department of Mathematics, University of Science and Technology of China, Hefei 230026, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2007年第1期189-192,共4页数学学报（英文版）

基　　金：NSF Grants 10471096,10571120 of China;"One Hundred Talents Program"from the University of Science and Technology of China

摘　　要：We show that the support of an irreducible weight module over the twisted Heisenberg-Virasoro algebra, which has an infinite-dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module are infinite dimensional. As a corollary, we obtain that every irreducible weight module over the twisted Heisenber-Virasoro algebra, having a nontrivial finite-dimensional weight space, is a Harish-Chandra module （and hence is either an irreducible highest or lowest weight module or an irreducible module from the intermediate series）.We show that the support of an irreducible weight module over the twisted Heisenberg-Virasoro algebra, which has an infinite-dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module are infinite dimensional. As a corollary, we obtain that every irreducible weight module over the twisted Heisenber-Virasoro algebra, having a nontrivial finite-dimensional weight space, is a Harish-Chandra module （and hence is either an irreducible highest or lowest weight module or an irreducible module from the intermediate series）.

关 键 词：the twisted Heisenberg-Virasoro algebra weight modules support 

分 类 号：O241.6[理学—计算数学]