# Irreducible Representations of Nilpotent Lie algebras

By Lie's theorem all irreducible representations of a solvable Lie algebra over $\mathbb C$ are one dimensional. What are all irreducible representations of a nilpotent Lie algebra ?

• Every nilpotent Lie algebra is solvable; is there something more specific that you need about their representations? – guest Jan 3 '15 at 20:16