Lesson plan
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.
Article summary
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.
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