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- W1661849449 abstract "We reformed the tensor product theory of vertex operator algebras developed by Huang and Lepowsky so that we could apply it to all vertex operator algebras satisfying C_2-cofiniteness. We also showed that the tensor product theory develops naturally if we include not only ordinary modules, but also weak modules with a composition series of finite length (we call it an Artin module). In particular, we don't assume the semisimplicity of the weight operator L(0). Actually, without the assumption of rationality, a C_2-cofiniteness on V is enough to obtain the existence of a tensor product of two Artin modules and natural associativity of tensor products. Namely, the category of Artin modules becomes a braided tensor category. As an application of the tensor product theory under C_2-cofiniteness, we proved the rationality of some orbifold models. For example, if a vertex operator algebra V has a finite automorphism group and the fixed point vertex operator subalgebra V^G is C_2-cofinite, then for any irreducible V^{ }-module W, there is an element hin such that W is contained in some h-twisted V-module. Furthermore, if V^G is rational, then V^{ } is also rational for any gin G." @default.
- W1661849449 created "2016-06-24" @default.
- W1661849449 creator A5036273084 @default.
- W1661849449 date "2003-09-22" @default.
- W1661849449 modified "2023-09-27" @default.
- W1661849449 title "A theory of tensor products for vertex operator algebra satsifying C_2-cofiniteness" @default.
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