Flatness and Semi-Rigidity of Vertex Operator Algebras

Details Flatness and Semi-Rigidity of Vertex Operator Algebras Flatness and Semi-Rigidity of Vertex Operator Algebras

2011-04-25

arxiv.org/abs/1104.4675v1

Mathematics

Quantum Algebra

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

Scientific paper

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.

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