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

The Lie algebra consists of strictly upper-triangular matricesThe 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 $f_{RQ}{}^S=-1$.