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
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i2 : KillingForm(g,{1,0},{0,1})
1
o2 = -
3
o2 : QQ
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