Are Matching Commutation Relations Enough to Prove Lie Algebra Isomorphism?

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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!
 
Thread 'Derivation of equations of stress tensor transformation'

Thread 'Derivation of equations of stress tensor transformation'

Hello ! I derived equations of stress tensor 2D transformation. Some details: I have plane ABCD in two cases (see top on the pic) and I know tensor components for case 1 only. Only plane ABCD rotate in two cases (top of the picture) but not coordinate system. Coordinate system rotates only on the bottom of picture. I want to obtain expression that connects tensor for case 1 and tensor for case 2. My attempt: Are these equations correct? Is there more easier expression for stress tensor...
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