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If we write a $3\times3$ real orthogonal matrix close to identiy, we would get
\[ X = I + \Delta X \] and then orthogonality demands that $X$ should be real antisymmetric matrix.
That gives Lie algebra of $O(3)$.
If we repeat the same for SU(2) we would get $2\times2$ traceless hermitian matrices as the Lie algebra of
$SU(2)$.
A statement, that is often found in literature. is Lie algebra of $O(3)$ and $SU(2)$ are same
do you think that this is correct?
ToHide:
even
THIS IS CONTENT OF FIRST STEP
Response 1: The two are obviously different
Response 2: The two algebras are the same as angular momentum algebra
Response 3: As abstract algebra they are the same, there is no difference
step 2
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step4
One more step. This is step 4
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