Twisted representations of vertex operator algebras

1995/09/06 by Dong, Chongying, Li, Haisheng, Mason, Geoffrey · 10 citations
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.q-alg/9509005

Abstract

Let V be a vertex operator algebra and g an automorphism of finite order. We construct an associative algebra A_g(V) and a pair of functors between the category of A_g(V)-modules and a certain category of admissible g-twisted V-modules. In particular, these functors exhibit a bijection between the simple modules in each category. We give various applications, including the fact that the complete reducibility of admissible g-twisted modules implies both the finite-dimensionality of homogeneous spaces and the finiteness of the number of simple g-twisted modules.

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
• Descent Theory for Vertex Algebras
• Decreasing filtrations, C₂-algebra and twisted modules
• C_n-cofinite twisted modules for C₂-cofinite vertex operator algebras
• A class of vertex operator algebras generated by Virasoro vectors
• Affine vertex operator superalgebra L_sl(2|1)(k,0) at boundary admissible level
• Structure and representations of the coset vertex operator algebra C( L_\widehatosp(1|2)(2,0), L_\widehatosp(1|2)(1,0)^{⊗ 2})
• On rank-two parabolic-type vertex operator algebras

Related

• Twisted representations of vertex operator algebras and associative algebras
• Induced modules for vertex operator algebras
• Twisted representations of vertex operator superalgebras
• Associative algebras for (logarithmic) twisted modules for a vertex operator algebra
• Weight-one elements of vertex operator algebras and automorphisms of categories of generalized twisted modules