Weight Modules Over a Class of Graded Lie Algebras
Weight Modules Over a Class of Graded Lie Algebras
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DOI：
10.1007/s10468-013-9444-9
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发表时间：
2014-08
影响因子：
0.6
通讯作者：
Xuewen Liu;Xiangqian Guo
中科院分区：
文献类型：
--
作者：
Xuewen Liu;Xiangqian Guo
本文研究了Olivier Mathieu在对有限增长单分次李代数进行分类时引入的一类分次李代数上的权模。证明了具有有限维权空间的此类代数上的任意权重模都可以分解为三部分。作为结果，我们给出了不可分解和单权模的粗略描述。文中还给出了一些算例。
In this paper, we study weight modules over a class of graded Lie algebras, which were introduced by Olivier Mathieu when he classified simple graded Lie algebras of finite growth. We show that any weight module over such algebras with finite dimensional weight spaces can be decomposed into three parts. As a consequence, we give rough descriptions of indecomposable and simple weight modules. Some examples are also presented.