Exploring Nilpotent Lie Algebras: Examples and Properties

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I know that all Lie algebras comprised of strictly upper triangular matrices are nilpotent. It would seem that there are also nilpotent Lie algebras that are not comprised of strictly upper triangular matrices, but I can't think of any. Does anybody have any examples?
 
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You can apply a change of basis to a Lie algebra, can't you?
 
And there are always abelian lie algebras.
 

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