Simple Lie algebra
In algebra, a simple Lie algebra is a Lie algebra that is non-abelian and contains no nonzero proper ideals. The classification of real simple Lie algebras is one of the major achievements of Wilhelm Killing and Élie Cartan.
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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.
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