Integrable module

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

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