Determination of fusion rule for E6-type conformal field theory

We show that the fusion rule for the E6 model, which is constructed from the one for the A1(1) Kac-Moody algebra by naive extension, is not associative. Then by using the associativity as a guiding principle, we obtain two types of fusion rules, one is left-right symmetric and the other asymmetric. The latter contains parameters and cannot be factorized into left and right sectors except one special case. Al and Dl models are briefly discussed. (orig.)