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

Notes

1. Kac 1990, § 3.6.
2. Kac 1990, Lemma 3.5.

References

• Kac, Victor (1990). Infinite dimensional Lie algebras (3rd ed.). Cambridge University Press. ISBN 0-521-46693-8.

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