Flatness and Semi-Rigidity of Vertex Operator Algebras

Abstract

In vertex operator algebra theories, most of the general theorems are proved under the assumptions of rationality and C_2-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 C_2-cofinite vertex operator algebras. For example, we apply them to orbifold models and show that if g is a finite automorphism of a rational C_2-cofinite vertex operator algebra T of CFT-type with T'\cong T and a fixed point subVOA T^g is C_2-cofinite, then T^g is also rational.

29pages, we reorganized arXiv0906.1407, 0909.3665, math/0309350 into one with short proofs

References in corpus (2)

• Flatness of Tensor Products and Semi-Rigidity for $C_2$-cofinite Vertex Operator Algebras II
• A theory of tensor products for vertex operator algebra satsifying C_2-cofiniteness

Cited by in corpus (10)

• Schur-Weyl Duality for Heisenberg Cosets
• Cosets of affine vertex algebras inside larger structures
• Logarithmic conformal field theory, log-modular tensor categories and modular forms
• On the tensor structure of modules for compact orbifold vertex operator algebras
• A holomorphic vertex operator algebra of central charge $24$ whose weight one Lie algebra has type $A_{6,7}$
• Orbifolds of lattice vertex algebras under an isometry of order two
• Reverse orbifold construction and uniqueness of holomorphic vertex operator algebras
• On the definition and K-theory realization of a modular functor
• On rationality for $C_2$-cofinite vertex operator algebras
• Quantum dimensions and fusion products for irreducible V_Q^s-modules, where s is an isometry of Q with s^2=1