The relationship between skew group algebras and orbifold theory

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Let V be a simple vertex operator algebra and let G be a finite automorphism group of V. In [DY], it was shown that any irreducible V-module is a completely reducible Vᵍ-module where Vᵍ is the G-invariant sub-vertex operator algebra of V. In this paper, we give an alternative proof of this fact using the theory of skew group algebras. We also extend this result to any irreducible g-twisted V-module when g is in the center of G and V is a g-rational vertex operator algebra.