Solution
= Solution
The transformed generators are
$$
J'_1=-J_1,
\qquad J'_2=J_2,
\qquad J'_3=-J_3.
$$
For example,
$$
[J'_1,J'_2]=[-J_1,J_2]=-iJ_3=iJ'_3.
$$
The other two cyclic commutators work identically, so
$$
[J'_i,J'_j]=i\epsilon_{ijk}J'_k.
$$
Conjugation by $C$ is therefore an <automorphism of a Lie algebra>.