Local Systems of Twisted Vertex Operators, Vertex Operator Superalgebras and Twisted Modules
نویسنده
چکیده
We introduce the notion of “local system of ZT -twisted vertex operators” on a Z2-graded vector space M , generalizing the notion of local system of vertex operators [Li]. First, we prove that any local system of ZT -twisted vertex operators on M has a vertex superalgebra structure with an automorphism σ of order T with M as a σ-twisted module. Then we prove that for a vertex (operator) superalgebra V with an automorphism σ of order T , giving a σ-twisted V -module M is equivalent to giving a vertex (operator) superalgebra homomorphism from V to some local system of ZT twisted vertex operators on M . As applications, we study the twisted modules for vertex operator (super)algebras associated to some well-known infinitedimensional Lie (super)algebras and we prove the complete reducibility of ZT twisted modules for vertex operator algebras associated to standard modules for an affine Lie algebra.
منابع مشابه
On Z2-twisted representation of vertex operator superalgebras and the Ising model SVOA
We investigate a general theory of the Z2-twisted representations of vertex operator superalgebras. Certain one-to-one correspondence theorems are established. We also give an explicit realization of the Ising model SVOA and its Z2-twisted modules. As an application, we obtain the Gerald Höhn’s Babymonster SVOA VB♮ and its Z2-twisted module VB ♮ tw from the moonshine VOA V ♮ by cutting off the ...
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