Notes for AKT-091006/0:03:35

Example: Let the Lie algebra be $gl_{n}(k)$ (with $[\cdot ,\cdot ]$ being the commutator and $\left\langle A,B\right\rangle =tr(AB)$)

Let the representation $R$: $\rho :{\mathcal {G}}\rightarrow End(R),\rho ([A,B])=\rho (A)\circ \rho (B)-\rho (B)\circ \rho (A)$