Abstract
We show that the fusion rule for a modular invariant E7-type conformal field theory, which is constructed from the one for the A1(1) Kac-Moody algebra by naive extension, is not associative. Then by imposing further restrictions to this naive fusion rule, we obtain associative fusion rules for the E7-type conformal field theory. Unlike the case of an E6-type conformal field theory, these fusion rules cannot be factorized into left and right sectors.
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