| Classification of Irreducible Weight Modules with a Finite-dimensional Weight Space over Twisted Heisenberg-Virasoro Algebra |
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| 作者姓名： | Ran SHEN Yu Cai SU |
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| 作者单位： | [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 |
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| 基金项目： | Supported by NSF Grants 10471096, 10571120 of China and ＂0ne Hundred Talents Program＂ from the University of Science and Technology of China |
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| 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）.
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| 关 键 词： | 扭曲Heisenberg-Virasoro代数 权重模块 支撑 权重空间 |
| 收稿时间： | 5 December 2005 |
| 修稿时间： | 2005-12-052006-01-10 |
Classification of Irreducible Weight Modules with a Finite–dimensional Weight Space over Twisted Heisenberg–Virasoro Algebra |
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| Ran SHEN Yu Cai SU.Classification of Irreducible Weight Modules with a Finite-dimensional Weight Space over Twisted Heisenberg-Virasoro Algebra[J].Acta Mathematica Sinica,2007,23(1):189-192. |
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| Authors: | Ran Shen Yu Cai Su |
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| Institution: | (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 |
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| Abstract: | 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 Heisenberg–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).
*Supported by NSF Grants 10471096, 10571120 of China and “One Hundred Talents Program” from the University of Science and
Technology of China |
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| Keywords: | the twisted Heisenberg-Virasoro algebra weight modules support |
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