A family of non-weight modules over the super-Virasoro algebras
A family of non-weight modules over the super-Virasoro algebras
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超 Virasoro 代数上的一系列非权重模块
DOI：
10.1016/j.jalgebra.2019.11.025
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发表时间：
2020
影响因子：
0.9
通讯作者：
Xia Limeng
中科院分区：
文献类型：
--
作者：
Yang Hengyun;Yao Yufeng;Xia Limeng
本文构造了超Virasoro代数上的一族非权模。Ramond代数上的这些模当被限制为Cartan子代数h上的模时是秩为1的，而Neveu-Schwarz代数上的这些模当被限制为Cartan子代数H上的模时是秩为2的。我们得到了这类模是简单模的一个充要条件。此外，我们确定了这些模的同构类。最后，我们证明了这些模构成了Ramond型超Virasoro代数上秩为1的自由U（h）-模的一个完全分类，也构成了Neveu-Schwarz型超Virasoro代数上秩为2的自由U（H）-模的一个完全分类.
In this paper, a family of non-weight modules over the super-Virasoro algebras are constructed. These modules over the Ramond algebra are free of rank 1 when restricted as modules over the Cartan subalgebra h, while these modules over the Neveu-Schwarz algebra are free of rank 2 when restricted as modules over the Cartan subalgebra H. We obtain a sufficient and necessary condition for such modules to be simple. Moreover, we determine the isomorphism classes of these modules. Finally, we show that these modules constitute a complete classification of free U (h)-modules of rank 1 over the super-Virasoro algebra of Ramond type, and also constitute a complete classification of free U (H)-modules of rank 2 over the super-Virasoro algebra of Neveu-Schwarz type.