[1] Zhang Xiufu, Zhou Jianhua,. Generalized super-Virsoro algebras and their Verma modules [J]. Journal of Southeast University (English Edition), 2004, 20 (2): 245-250. [doi:10.3969/j.issn.1003-7985.2004.02.025]

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Generalized super-Virsoro algebras and their Verma modules()

广义Virasoro超代数及其Verma模

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

20

Issue:

2004 2

Page:

245-250

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2004-06-30

Info

Title:

Generalized super-Virsoro algebras and their Verma modules

广义Virasoro超代数及其Verma模

Author(s):

Zhang Xiufu;  Zhou Jianhua

Department of Mathematics, Southeast University, Nanjing 210096, China

张秀福;  周建华

东南大学数学系, 南京 210096

Keywords:

Lie algebra;  module;  isomorphism

李代数;  模;  同构

PACS:

O151.2;O152.5

DOI:

10.3969/j.issn.1003-7985.2004.02.025

Abstract:

For any additive subgroup M of a field F and α∈F such that 2α∈M, there are two classes of generalized super-Virasoro algebras denoted by SVir [M, α] and SVir^~ [M, α] by Su and Zhao. The latter is in fact a trivial extension of the former. In this paper, based on the discussion on isomorphisms, the Verma modules of Svir [M, α] are studied, and the irreducibility of these modules are obtained.

对域F的加法子群M以及α∈F, 且2α∈M, 苏育才及赵开明定义了2类广义Virasoro超代数, 它们分别被记成SVir[M, α]和SVir^~[M, α], 后者是前者的平凡扩张. 基于对同构的讨论, 研究了SVir[M, α]的Verma模, 并且得到了这些模的不可约性.

References:

[1] Djokovi c’D, Zhao K. Derivations, isomorphisms and second cohomology of generalized Witt algebras [J]. Trans Am Math Soc, 1998, 350(2): 643-664.
[2] Patera J, Zassenhaus H. The high rank Virasoro algebras [J]. Comm Math Phys, 1991, 136: 1-14.
[3] Su Y, Zhao K. Generalized Virasoro and super-Virasoro algebras and modules of intermediate series [J]. J Alg, 2002, 252: 1-19.
[4] Hu J, Wang X, Zhao K. Verma modules over generalized Virasoro algebras Vir[G][J]. J Pure and Appl Alg, 2003, 177: 61-69.
[5] Su Y. Harish-Chandra modules of the intermediate series over the high rank Virasoro algebras and high rank super-Virasoro algebras [J]. J Math Phys, 1994, 35(4): 2013-2023.
[6] Mathieu O. Classification of Harish-Chandra modules over the Virasoro Lie algebras [J]. Invent Math, 1992, 107: 225-234.
[7] Su Y. Classification of Harish-Chandra modules over the super-Virasoro algebras [J]. Comm Alg, 1995, 23(10): 3653-3675.
[8] Kaplansky I, Satharoubane L J. Harish-Chandra modules over the Virasoro algebra[J]. MSRI Publ, 1987, 4: 217-231.
[9] Martin C, Piard A. Indecomposable modules over the Virasoro Lie algebra and a conjecture of V. Kac [J]. Comm Math Phys, 1991, 137: 109-132.

Memo

Memo:

Biographies: Zhang Xiufu(1975—), male, master; Zhou Jianhua(corresponding author), male, associate professor, jhzhou@seu.edu.cn.

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