Integrable module

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.

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