# Simple Lie algebra

In algebra, a **simple Lie algebra** is a Lie algebra that is nonabelian and contains no nonzero proper ideals. The classification of real simple Lie algebras is one of major achievements of Wilhelm Killing and Élie Cartan.

A direct sum of simple Lie algebras is called a semisimple Lie algebra.

A simple Lie group is a connected Lie group whose Lie algebra is simple.

where *n* is the number of the nodes (the simple roots). The correspondence of the diagrams and complex simple Lie algebras is as follows:^{[2]}