顶点算子超代数及相关的结合代数的表示

数学物理学报 ›› 2009, Vol. 29 ›› Issue (4): 1022-1032.

顶点算子超代数及相关的结合代数的表示

(1.上海交通大学数学系, 上海 200240, 2.常熟理工学院数学系, 江苏常熟 215500)

收稿日期:2007-09-21 修回日期:2008-04-18 出版日期:2009-08-25 发布日期:2009-08-25
基金资助:
国家自然科学基金(10671027, 10871125)和江苏省高校自然科学基础研究基金(08KJD110001)资助

Representations of Vertex Operator Superalgebras and Associative Algebras

(1.Department of |Mathematics, Shanghai Jiaotong University, Shanghai 200240, 2.Department of |Mathematics, Changshu Institute of Technology, Jiangsu, Changshu 215500)

Received:2007-09-21 Revised:2008-04-18 Online:2009-08-25 Published:2009-08-25
Supported by:
国家自然科学基金(10671027, 10871125)和江苏省高校自然科学基础研究基金(08KJD110001)资助

摘要/Abstract

摘要：

设 V 是一个顶点算子超代数. 该文得到了一系列的结合代数A_n(V)(对任何n ∈ 1/2 + Z₊(i ∈ {0,1})). 也给出了A_n(V) -模但非A_n_-1/2(V) -模的不可约模范畴和单的可容许的V -模的范畴之间的一一对应关系. 对于给定的A_n(V) -模但非A_n_-1/2(V) -模U, 还构造了一类广义Verma可容许的V -模M_n(U). 进而利用结合代数的表示进一步研究了顶点算子超代数的表示论.

关键词: 顶点算子代数, 表示论, 顶点算子超代数, 结合代数

Abstract:

Let V be a vertex operator superalgebra. The authors construct a sequence of associative algebra A_n(V) for n ∈ 1/2 Z₊. It is also exposed that there is a pair of functors between the category of A_n(V)-modules which are not _An-1/2(V)-modules and the category of admissible V-modules. The functors exhibit a bijection between the simple modules in each category. They also construct a generalized Verma admissible V-module M_n(U) by a A_n(V)-module which is not A_n_-1/2(V)-module U. Futhermore, they study the theory of representations of vertex operator superalgebra by associative algebra A_n(V).

Key words: Vertex operator algebras, Representation theory, Vertex operator superalgebras, Associative algebras

中图分类号:

17B69

姜伟, 蒋启芬, 姜翠波. 顶点算子超代数及相关的结合代数的表示[J]. 数学物理学报, 2009, 29(4): 1022-1032.

JIANG Wei, JIANG Qi-Fen, JIANG Cui-Bo. Representations of Vertex Operator Superalgebras and Associative Algebras[J]. Acta mathematica scientia,Series A, 2009, 29(4): 1022-1032.

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