Research and Construction of Vertex Operator Algebras of finite type

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One of important problem on Conformal Field Theory (Vertex Operator Algebra) is to construct one of finite type. One of the candidates to construct one of finite type is an orbifold theory using a finite automorphism group, but it is not easy to treat. In this research, we succeed to prove the hereditary of C2-cofiniteness under the orbifold theory for a finite cyclic automorphism, which is the main purpose of this research. By this result, an orbifold construction of holomorphic vertex operator algebras becomes problems to check the weights and fusion rules. As application, several researchers succeeded to construct new holomorphic vertex operator algebra using this result.