A Family of Non-weight Modules over the Virasoro Algebra

被引：0

作者：

Chen, Guobo ^{[1
]}

机构：

[1] Tongji Univ, Sch Math Sci, Shanghai 200092, Peoples R China

来源：

ALGEBRA COLLOQUIUM | 2020年 / 27卷 / 04期

关键词：

Virasoro algebra; non-weight module; simple module; IRREDUCIBLE REPRESENTATIONS; LIE-ALGEBRA; CLASSIFICATION; FINITE;

D O I：

10.1142/S100538672000067X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the tensor product modules of a class of non- weight modules and highest weight modules over the Virasoro algebra. We determine the necessary and sufficient conditions for such modules to be simple and the isomorphism classes among all these modules. Finally, we prove that these simple non-weight modules are new if the highest weight module over the Virasoro algebra is non-trivial.

引用

页码：807 / 820

页数：14

共 21 条

[1]

[Anonymous], 2008, CONFORMAL FIELD

[2] Blocks and modules for Whittaker pairs [J].

Batra, Punita ;

Mazorchuk, Volodymyr .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2011, 215 (07) :1552-1568

[3] THE IRREDUCIBLE REPRESENTATIONS OF THE LIE-ALGEBRA SL(2) AND OF THE WEYL ALGEBRA [J].

BLOCK, RE .

ADVANCES IN MATHEMATICS, 1981, 39 (01) :69-110

[4] A CLASS OF SIMPLE NON-WEIGHT MODULES OVER THE VIRASORO ALGEBRA [J].

Chen, Haibo ;

Han, Jianzhi .

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2020, 63 (04) :956-970

[5] A class of simple weight modules over the twisted Heisenberg-Virasoro algebra [J].

Chen, Haibo ;

Han, Jianzhi ;

Su, Yucai .

JOURNAL OF MATHEMATICAL PHYSICS, 2016, 57 (10)

[6] Tensor product weight modules over the Virasoro algebra [J].

Chen, Hongjia ;

Guo, Xiangqian ;

Zhao, Kaiming .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2013, 88 :829-844

[7] A family of irreducible representations of the Witt Lie algebra with infinite-dimensional weight spaces [J].

Conley, CH ;

Martin, C .

COMPOSITIO MATHEMATICA, 2001, 128 (02) :153-175

[8]

Goddard P., 1986, Int. J. Mod. Phys. A, V1, P303

[9]

Han J., ARXIV170807272

[10]

Kac VG, 1990, INFINITE DIMENSIONAL

← 1 2 3 →