Let g be a Lie algebra. The Killing form on g is the symmetric bilinear form given by (x,y) = Tr(ad x ad y). It can restricted to a Cartan subalgebra h and transfered to h^{*}, yielding a symmetric bilinear form on weights. One popular convention is to scale the Killing form so that (θ,θ) =2, where θ is the highest root.
i1 : g=simpleLieAlgebra("A",2) o1 = g o1 : LieAlgebra |
i2 : KillingForm(g,{1,0},{0,1}) 1 o2 = - 3 o2 : QQ |