Simple Lie group

Summary

A simple Lie group is a connected Lie group whose Lie algebra is a simple Lie algebra. Such a Lie algebra is not abelian and has no ideals other than $0$ and itself. Simple Lie groups are the building blocks of the semisimple Lie groups, and through them of a large part of Lie theory. Up to coverings and central quotients, they are classified by the simple Lie algebras. These form the classical families $A_n, B_n, C_n, D_n$ and five exceptional types.