Editing Simple Lie group (section)

===Semisimple Lie groups===
A '''semisimple''' Lie group is a connected Lie group so that its only [[closed subgroup|closed]] [[Connected space|connected]] [[Abelian group|abelian]] [[normal subgroup|normal]] subgroup is the trivial subgroup. Every simple Lie group is semisimple. More generally, any product of simple Lie groups is semisimple, and any quotient of a semisimple Lie group by a closed subgroup is semisimple. Every semisimple Lie group can be formed by taking a product of simple Lie groups and quotienting by a subgroup of its center. In other words, every semisimple Lie group is a [[central product]] of simple Lie groups. The semisimple Lie groups are exactly the Lie groups whose Lie algebras are [[semisimple Lie algebra]]s.