KillingForm(g,v,w)
Let $\mathbf{g}$ be a Lie algebra. The Killing form on $\mathbf{g}$ is the symmetric bilinear form given by $(x,y) = Tr(ad x ad y)$. It can restricted to a Cartan subalgebra $\mathbf{h}$ and transferred to $\mathbf{h}^*$, yielding a symmetric bilinear form on weights. One popular convention is to scale the Killing form so that $(\theta,\theta) =2$, where $\theta$ is the highest root.


The object KillingForm is a method function.