Quantum Dimensions and Quantum Galois Theory
classification
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math.OA
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quantumdimensionsoperatorvertexalgebrasrationalgaloistheory
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The quantum dimensions of modules for vertex operator algebras are defined and their properties are discussed. The possible values of the quantum dimensions are obtained for rational vertex operator algebras. A criterion for simple currents of a rational vertex operator algebra is given. A full Galois theory for rational vertex operator algebras is established using the quantum dimensions.
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