| 顶点算子超代数及相关的结合代数的表示 |
| |
| 引用本文： | 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(A辑),2009,29(4):1022-1032. |
| |
| 作者姓名： | 姜伟 蒋启芬 姜翠波 |
| |
| 作者单位： | 姜伟(上海交通大学数学系,上海,200240;常熟理工学院数学系,江苏常熟,215500);蒋启芬,姜翠波(上海交通大学数学系,上海,200240) |
| |
| 基金项目： | 国家自然科学基金，江苏省高校自然科学基础研究基金 |
| |
| 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An(V)(对任何n∈ 1/2 + Z+(i∈ {0,1})). 也给出了An(V) -模但非An-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An(V) -模但非An-1/2(V) -模U, 还构造了一类广义Verma可容许的V -模Mn(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 |
| 收稿时间： | 2007-09-21 |
| 修稿时间： | 2008-04-18 |
Representations of Vertex Operator Superalgebras and Associative Algebras |
| |
| Institution: | (1.Department of |Mathematics, Shanghai Jiaotong University, Shanghai 200240, 2.Department of |Mathematics, Changshu Institute of Technology, Jiangsu, Changshu 215500) |
| |
| Abstract: | Let V be a vertex operator superalgebra. The authors construct a sequence of associative algebra An(V) for n ∈ 1/2 Z+. It is also exposed that there is a pair of functors between the category of An(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 Mn(U) by a An(V)-module which is not An-1/2(V)-module U. Futhermore, they study the theory of representations of vertex operator superalgebra by associative algebra An(V). |
| |
| Keywords: | Vertex operator algebraszz Representation theoryzz Vertex operator superalgebraszz Associative algebraszz |
| 本文献已被 万方数据 等数据库收录！ |
| 点击此处可从《数学物理学报(A辑)》浏览原始摘要信息 |
| 点击此处可从《数学物理学报(A辑)》下载免费的PDF全文 |
|
