Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 302 / 4 / a / ii

For a Cartan subalgebra $\mathfrak{h}$, the root set consists of the nonzero linear functionals $\alpha \in {\mathfrak{h}}^{\ast }$ for which ${\mathfrak{g}}_{\alpha }=\{X:[H,X]=\alpha (H)X\}$ is nonzero. It is the root system of the Lie algebra.