Integrable module

In algebra, an integrable module 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.[1] For example, the adjoint representation of a Kac–Moody algebra is integrable.[2]

References

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

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