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.
where n is the number of the nodes (the simple roots). The correspondence of the diagrams and complex simple Lie algebras is as follows: