In algebra, a simple Lie algebra is a Lie algebra that is non-abelian and contains no nonzero proper ideals.
A simple Lie algebra cannot be a solvable Lie algebra.
A direct sum of simple Lie algebras is called a semisimple Lie algebra. A Lie algebra is semisimple if and only if its radical of a Lie algebra is 0.
A simple Lie group is a connected Lie group whose Lie algebra is simple.
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Author of the notes: Antonio J. Pan-Collantes
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