integrable module

{{one source |date=May 2024}}

In algebra, an integrable module (or integrable representation) of a Kac–Moody algebra $\backslash mathfrak\; g$ (a certain infinite-dimensional Lie algebra) is a representation of $\backslash mathfrak\; g$ such that (1) it is a sum of weight spaces and (2) the Chevalley generators $e\_i,\; f\_i$ of $\backslash mathfrak\; g$ are locally nilpotent.{{harvnb|Kac|1990|loc=§ 3.6.}} For example, the adjoint representation of a Kac–Moody algebra is integrable.{{harvnb|Kac|1990|loc=Lemma 3.5.}}