Integrable module

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