Acta mathematica scientia,Series A ›› 2009, Vol. 29 ›› Issue (4): 1022-1032.

• Articles • Previous Articles     Next Articles

Representations of Vertex Operator Superalgebras and Associative Algebras

  

  1. (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

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).

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

CLC Number: 

  • 17B69
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