Irreducible tensor product modules over the affine-Virasoro algebra of type A1

被引：5

作者：

Chen, Qiu-Fan ^{[1
]}

Yao, Yu-Feng ^{[1
]}

机构：

[1] Shanghai Maritime Univ, Dept Math, Shanghai 201306, Peoples R China

来源：

LINEAR & MULTILINEAR ALGEBRA | 2022年 / 70卷 / 22期

基金：

中国国家自然科学基金;

关键词：

Affine-Virasoro algebra; tensor product; non-weight module; highest weight module; WEIGHT MODULES; REPRESENTATIONS; FINITE; CLASSIFICATION;

D O I：

10.1080/03081087.2021.1998309

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we construct a class of non-weight modules over the affine-Virasoro algebra of type A(1) by taking the tensor product of irreducible U(h)-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 A(1), and give sufficient and necessary conditions for these induced modules to be reducible.

引用

页码：7558 / 7574

页数：17

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