Integrable module

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

External links

• Kac, Victor (1990). Infinite dimensional Lie algebras (3rd ed.). Cambridge University Press. ISBN 0-521-46693-8. https://books.google.com/books?id=kuEjSb9teJwC&q=Victor%20G.%20Kac&pg=PP1.