Casimir element

Given a simple Lie algebra $$\mathfrak{g}$$over the field $$\mathbb{C}$$ of complex numbers, the Casimir element is an element in the universal enveloping algebra $$U(\mathfrak{g})$$ that commutes with every other element there. In fact it generates the whole centre of the algebra. It is constructed from the invariant bilinear form (Cartan-Killing form) and is pivotal in the structure theory of representations of Lie algebras.

homework

 * 1) write down the casimir element for sl2 and show that it commutes with the standard generators e,f,h.