How do you show Lie algebra is semisimple?

If R(g) is 0, then g is a finitedimensional Lie algebra.

What is a semisimple group?

A Lie algebra is a Lie algebra that is a direct sum of Lie algebras.

Are Lie algebras groups?

Every finite-dimensional Lie algebra is the Lie algebra of a Lie group according to Lie’s third theorem.

What is a simple Lie?

It is said that a Lie algebra is simple if it is not a lie.

Are Lie algebras groups?

Every finite-dimensional Lie algebra is the Lie algebra of a Lie group according to Lie’s third theorem.

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