A family of simple weight modules over the Virasoro algebra
A family of simple weight modules over the Virasoro algebra
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Virasoro 代数上的一系列简单权重模块
DOI：
10.1016/j.jalgebra.2017.02.004
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发表时间：
2017
影响因子：
0.9
通讯作者：
Zhao Kaiming
中科院分区：
文献类型：
--
作者：
Lu Rencai;Zhao Kaiming
利用多项式代数C [t]的导子李代数C [t] ddt上的单模，构造了Witt代数上的权空间为无穷维的新的权模.我们确定了这些新的模是简单的必要和充分条件，以及确定两个Witt模同构的必要和充分条件。如果一个模不是简单的，我们得到它的所有子模。因此，我们完全确定了由[3]定义的Witt模的单纯性和同构类，这是本研究中构造的模的一小部分。
Using simple modules over the derivation Lie algebra C [t] d d t for the polynomial algebra C [t], we construct new weight modules over the Witt algebra where all the weight spaces are infinite dimensional. We determine the necessary and sufficient conditions for these new modules being simple, as well as determining the necessary and sufficient conditions for two Witt modules being isomorphic. If a module is not simple, we obtain all its submodules. As a consequence, we fully determine the simplicity and isomorphism classes for the Witt modules defined by [3], which are a small proportion of the modules constructed in this study.