 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-302/2/c/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Since

(ad_{T_{a}})^{c}_{b} = f_{ab}^{c}

, the Killing form has components

κ_{ab} = f_{a c}^{d} f_{b d}^{c} .

This is the matrix trace of

ad_{T_{a}} ad_{T_{b}}

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