Classification of Irreducible Weight Modules with a Finite–dimensional Weight Space over Twisted Heisenberg–Virasoro Algebra
Classification of Irreducible Weight Modules with a Finite–dimensional Weight Space over Twisted Heisenberg–Virasoro Algebra
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DOI：
10.1007/s10114-005-0807-y
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发表时间：
2005-12
期刊：
影响因子：
--
通讯作者：
Ran Shen;Yu-cai Su
中科院分区：
文献类型：
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作者：
Ran Shen;Yu-cai Su
我们证明了不可约权重模块在具有无限维权重空间的扭曲海森堡-维拉索罗代数上的支持与权重格一致，并且该模块的所有非平凡权重空间都是无限维的。作为推论，我们得到扭曲的 Heisenberg-Virasoro 代数上的每个不可约权重模块，具有非平凡的有限维权重空间，都是 Harish-Chandra 模块（因此要么是不可约的最高或最低权重模块，要么是来自中间级数的不可约模块）。
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).