Twisted representations of vertex operator algebras and associative algebras

1997/02/21 by C. Dong, H. Li, Dong, C. +3 · 5 citations
Mathematics · #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #q-alg

paper · pdf · doi:10.48550/arxiv.q-alg/9702027

latex, 9 pages

arxiv created 1997/02/21 · arxiv updated 2009/11/30

Abstract

Let V be a vertex operator algebra and g an automorphism of order T. We construct a sequence of associative algebras A_g,n(V) with n∈(1)/(T)\Z nonnegative such that A_g,n(V) is a quotient of A_g,n+1/T(V) and a pair of functors between the category of A_g,n(V)-modules which are not A_g,n-1/T(V)-modules and the category of admissible V-modules. These functors exhibit a bijection between the simple modules in each category. We also show that V is g-rational if and only if all A_g,n(V) are finite-dimensional semisimple algebras.

Cited by

• Twisted bimodules and associative algebras associated to VOAs
• Twisted ϕ-coordinated modules for vertex algebras and Zhu's correspondence theorem
• Twisted associative algebras associated to vertex algebras
• Refining twisted bimodules associated to VOAs
• Twisted regular representations and bimodules in vertex operator algebra theory

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• Twisted representations of vertex operator algebras
• Vertex operator algebras and associative algebras
• Bimodules and g-rationality of vertex operator algebras
• Twisted representations of vertex operator superalgebras
• Representations of vertex operator algebras