Non-weight modules over algebras related to the Virasoro algebra

被引：16

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：

JOURNAL OF GEOMETRY AND PHYSICS | 2018年 / 134卷

基金：

上海市自然科学基金; 中国国家自然科学基金;

关键词：

Virasoro algebra; Loop-Virasoro algebra; Block type Lie algebra; Non-weight module; Simple module; HARISH-CHANDRA MODULES; LIE-ALGEBRAS; QUASIFINITE REPRESENTATIONS; IRREDUCIBLE MODULES; CLASSIFICATION; FAMILY;

D O I：

10.1016/j.geomphys.2018.08.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study some non-weight modules over the loop-Virasoro algebra (sic) and Block type Lie algebras B(q), where q is a nonzero complex number. Those modules when restricted to the Cartan subalgebra (modulo center) are free of rank one. We provide a sufficient and necessary condition for such modules to be simple, and determine their isomorphism classes. Moreover, we obtain the simplicity of modules over loop-Virasoro algebras by taking tensor products of some irreducible modules mentioned above with irreducible highest weight modules or Whittaker modules. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：11 / 18

页数：8

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