Uniform product of A n , g ( V ) for an orbifold model V and G - twisted Zhu algebra

Let V be a simple vertex operator algebra and G a finite automorphism group of V . It was shown in [DY] that any irreducible V -module is a completely reducible V G-module. In this paper, we show that any g-twisted V -module is also a completely reducible V G-module if V is g-rational. For each g ∈ G, a g-twisted Zhu algebra Ag,n(V ) plays an important role, but the given product in Ag,n(V ) depends on the eigenspaces of g. We show that there is a uniform definition of products on V and we introduce a universal G-twisted Zhu algebra which covers all g-twisted Zhu algebras.