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>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 302 / 2 / c / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/iii/paper-302/2/c/solution