Integrable module

In algebra, an integrable module (or integrable representation) of a Kac–Moody algebra formula_1 (a certain infinite-dimensional Lie algebra) is a representation of formula_1 such that (1) it is a sum of weight spaces and (2) the Chevalley generators formula_3 of formula_1 are locally nilpotent. For example, the adjoint representation of a Kac–Moody algebra is integrable.