Simple weight modules over weak generalized Weyl algebras
Simple weight modules over weak generalized Weyl algebras
复制标题
弱广义韦尔代数上的简单权重模块
DOI：
10.1016/j.jpaa.2014.12.003
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发表时间：
2015
影响因子：
0.8
通讯作者：
Zhao Kaiming
中科院分区：
文献类型：
--
作者：
Lu Rencai;Mazorchuk Volodymyr;Zhao Kaiming
在本文中，我们解决了弱广义Weyl 代数上的简单权重模块的分类问题。弱广义Weyl 代数和广义Weyl 代数之间的主要区别在于，弱广义Weyl 代数是使用交换环R 的自同态而不是自同构来定义的。我们将弱广义外尔代数上的简单权重模块的分类简化为描述上述自同态在最大理想集上的作用的动力学。我们还描述了我们的结果在广义海森堡代数研究中的应用。
In this paper we address the problem of classification of simple weight modules over weak generalized Weyl algebras of rank one. The principal difference between weak generalized Weyl algebras and generalized Weyl algebras is that weak generalized Weyl algebras are defined using an endomorphism rather than an automorphism of a commutative ringR. We reduce classification of simple weight modules over weak generalized Weyl algebras to description of the dynamics of the action of the above mentioned endomorphism on the set of maximal ideals. We also describe applications of our results to the study of generalized Heisenberg algebras.