Non-diagonal modular invariants and extensions of Kac-Moody algebras

We explicitly show that all non-diagonal modular invariants of Kac-Moody algebras which are generated by a simple current with conformal weight one are equivalent to the diagnoal modular invariant of an enlarged Kac-Moody algebra. For simple currents with higher integer weight, the associated non-diagonal modular invariants do not, in general, correspond to a larger Kac-Moody algebra. This indicates the existence of non-trivial generalisations of the affine algebras. (orig.)