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- W1533643192 abstract "We study properties of a C_2-cofinite vertex operator algebra of CFT type. If it is also rational and V'cong V, then the rigidity of the tensor category of modules has been proved by Huang. When we treat an irrational C_2-cofinite VOA, the rigidity is too strong, because it is almost equivalent to be rational as we see. We introduce a natural weaker condition semi-rigidity. Under this condition, we prove the following results. For a projective cover P of a V-module V and a finitely generated V-module M, the projective cover of M is a direct summand of the tensor product Pboxtimes M defined by logarithmic intertwining operators. Using this result, we prove the flatness property of finitely generated modules for the tensor products, that is, if 0to Ato Bto Cto 0 is exact then so is 0to Dboxtimes Ato Dboxtimes Bto Dboxtimes Cto 0 for any finitely generated V-modules A, B, C and D. As a corollary, we have that if a semi-rigid C_2-cofinite V contains a rational subVOA with the same Virasoro element, then V is rational." @default.
- W1533643192 created "2016-06-24" @default.
- W1533643192 creator A5036273084 @default.
- W1533643192 date "2009-06-08" @default.
- W1533643192 modified "2023-09-27" @default.
- W1533643192 title "Flatness of Tensor Products and Semi-Rigidity for $C_2$-cofinite Vertex Operator Algebras II" @default.
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