Simple Lie algebra

Summary

A simple Lie algebra is a non-abelian Lie algebra whose only ideals are $0$ and itself. Simple Lie algebras are the building blocks of semisimple Lie algebras, which are direct sums of them in characteristic $0$. Over $\C$ the finite-dimensional simple Lie algebras are classified: four infinite families $A_n$, $B_n$, $C_n$, $D_n$ and five exceptional algebras $E_6$, $E_7$, $E_8$, $F_4$, $G_2$.