Casimir invariant C_2 = Σ T^a T_a in centre of U(g)

For a semisimple Lie algebra g with non-degenerate Killing form g_{ab}, the quadratic Casimir operator C_2 = g^{ab}·T_a·T_b (contraction with inverse Killing form) lies in the centre of the universal enveloping algebra U(g). Commutation…