Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 302 / 2 / b / i / Solution

Conjugation differentiates to the Adjoint representationBecause conjugations compose, ${\mathrm{Ad}}_{gh}={\mathrm{Ad}}_g{\mathrm{Ad}}_h$ and ${\mathrm{Ad}}_e=I$, so this is a group representation.