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Rationality of vertex operator algebras

Chongying Dong·Cuipo Jiang
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Abstract

It is shown that a simple vertex operator algebra V is rational if and only if its Zhu algebra A(V) is semisimple and each irreducible admissible V-module is ordinary. A contravariant form on a Verma type admissible V-module is constructed and the radical is exactly the maximal proper submodule. As an application the rationality of V_L^+ for any positive definite even lattice is obtained.

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Chongying Dong, Cuipo Jiang. 2006-07-26. Rationality of vertex operator algebras. https://arxiv.org/abs/math/0607679

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