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Weight Modules Over a Class of Graded Lie Algebras

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, Henan Province, People’s Republic of China

    Xuewen Liu & Xiangqian Guo

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  1. Xuewen Liu
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  2. Xiangqian Guo
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Correspondence to Xiangqian Guo.

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Liu, X., Guo, X. Weight Modules Over a Class of Graded Lie Algebras. Algebr Represent Theor 17, 1235–1248 (2014). https://doi.org/10.1007/s10468-013-9444-9

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  • DOI: https://doi.org/10.1007/s10468-013-9444-9

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