The Lie algebra consists of strictly upper-triangular matrices
$$
X=qQ+rR+sS,
\quad Q=E_{12},\quad R=E_{23},\quad S=E_{13}.
$$
The only nonzero basis bracket is $[Q,R]=S$. Thus the independent nonzero <structure constant of a Lie algebra> values are $f_{QR}{}^S=1$ and $f_{RQ}{}^S=-1$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 302 / 1 / b / ii / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-302/1/b/ii/solution