Rationality of vertex operator algebras

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.

33pages

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• Vertex Algebras and Algebraic Curves
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Cited by in corpus (4)

• The N=1 triplet vertex operator superalgebras
• Classification of irreducible modules of the vertex algebra $V_L^{+}$ when $L$ is a nondegenerate even lattice of an arbitrary rank
• Bimodules and g-rationality of vertex operator algebras
• Rationality of the vertex algebra $V_L^{+}$ when $L$ is a nondegenerate even lattice of arbitrary rank