Example
- Every abelian Lie algebra is solvable.
- Every nilpotent Lie algebra is solvable.
- Every Lie subalgebra, quotient and extension of a solvable Lie algebra is solvable.
- Let be a subalgebra of consisting of upper triangular matrices. Then is solvable.
Read more about this topic: Solvable Lie Algebra
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“Our intellect is not the most subtle, the most powerful, the most appropriate, instrument for revealing the truth. It is life that, little by little, example by example, permits us to see that what is most important to our heart, or to our mind, is learned not by reasoning but through other agencies. Then it is that the intellect, observing their superiority, abdicates its control to them upon reasoned grounds and agrees to become their collaborator and lackey.”
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