Flatness and Semi-Rigidity of Vertex Operator Algebras

Original · EN

In vertex operator algebra theories, most of the general theorems are proved under the assumptions of rationality and C₂-cofiniteness. In this paper, we obtain several general theorems without the assumption of rationality so that we can use them for proving rationality of given C₂-cofinite vertex operator algebras. For example, we apply them to orbifold models and show that if g is a finite automorphism of a rational C₂-cofinite vertex operator algebra T of CFT-type with T' T and a fixed point subVOA Tᵍ is C₂-cofinite, then Tᵍ is also rational.