Bimodules and g-rationality of vertex operator algebras

2006/07/28 by Dong, Chongying, Jiang, Cuipo · 3 citations
#17B69 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.math/0607758

Abstract

This paper studies the twisted representations of vertex operator algebras. Let V be a vertex operator algebra and g an automorphism of V of finite order T. For any m,n in (1/T)Z₊, an A_g,n(V)-A_g,m(V)-bimodule A_g,n,m(V) is constructed. The collection of these bimodules determines any admissible g-twisted V-module completely. A Verma type admissible g-twisted V-module is constructed naturally from any A_g,m(V)-module. Furthermore, it is shown with the help of bimodule theory that a simple vertex operator algebra V is g-rational if and only if its twisted associative algebra A_g(V) is semisimple and each irreducible admissible g-twisted V-module is ordinary.

Cited by

• Twisted bimodules and associative algebras associated to VOAs
• Twisted ϕ-coordinated modules for vertex algebras and Zhu's correspondence theorem
• Cofiniteness for Twisted Fusion Products in Vertex Operator Algebra Theory

Related

• Twisted representations of vertex operator algebras and associative algebras
• Representations of vertex operator algebras
• Representations of vertex operator algebras and bimodules
• Twisted representations of vertex operator superalgebras
• Bimodules associated to vertex operator algebras