Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 102 / 3 / b / v / Solution

The preceding Dynkin diagram identifies the root system $D_3$ with $A_3$. The classification of finite-dimensional complex Simple Lie algebras by connected Dynkin diagrams therefore givesThis is the Isomorphism between so6 and sl4. Both algebras have dimension $15$, consistently with the classification.