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

• Notes

• References

cite-note-11. ↑ Kac 1990, § 3.6.

cite-note-22. ↑ Kac 1990, Lemma 3.5.

• citerefkac1990Kac, Victor (1990). Infinite dimensional Lie algebras (3rd ed.). Cambridge University Press. ISBN 0-521-46693-8.