Notes for AKT-091006/0:11:24

Choose basis $(X_{a})$, $a\in \{1,2,\cdots ,\dim({\mathcal {G}})\}$ for ${\mathcal {G}}$ and basis $(e_{a})$, $a\in \{1,2,\cdots ,\dim(R)\}$ for $R$

express all Lie-algebra operations in terms of the basis.