Are Matching Commutation Relations Enough to Prove Lie Algebra Isomorphism?

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SUMMARY

To prove that two Lie algebras are isomorphic, it is sufficient to demonstrate that their generators fulfill the same commutation relations. This conclusion is definitive and can be established through a straightforward proof. Participants in the discussion confirmed this understanding, emphasizing the importance of commutation relations in Lie algebra theory.

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parton
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Hi!

I just need a "yes" or "no" answer.

If i have to show that two lie algebras are isomorphic,
is it sufficient to show that their generators fulfill the same commutation relations?
 
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Yes. It's not hard to prove this, so I recommend it as an exercise.
 
Ok, Thanks!
 

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