Irreducible tensor product modules over the affine-Virasoro algebra of type $A_1$
Irreducible tensor product modules over the affine-Virasoro algebra of type $A_1$
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A(1) 型仿射-Virasoro 代数上的不可约张量积模
DOI：
10.1080/03081087.2021.1998309
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发表时间：
2021
影响因子：
1.1
通讯作者：
Yao Yu-Feng
中科院分区：
文献类型：
--
作者：
Chen Qiu-Fan;Yao Yu-Feng
本文在仿射- virasoro型代数上构造了一类非权模，方法是取秩为1的不可约自由模与不可约最高权模的张量积。确定了这些模块的不可约性和同构类。此外，我们还证明了这些张量积模不同于已知的非权重模。最后，我们从仿射- virasoro型代数的子代数上的模实现了一些张量积模为诱导模，并给出了这些诱导模可约的充要条件。
In this paper, we construct a class of non-weight modules over the affine-Virasoro algebra of typeby taking the tensor product of irreducible-free modules of rank 1 with irreducible highest weight modules. The irreducibility and the isomorphism classes of these modules are determined. Moreover, we show that these tensor product modules are different from the known non-weight modules. Finally, we realize some tensor product modules as induced modules from modules over certain subalgebras of the affine-Virasoro algebra of type, and give sufficient and necessary conditions for these induced modules to be reducible.