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LieTypes :: KillingForm

KillingForm -- computes the scaled Killing form applied to two weights

Synopsis

Description

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

Ways to use KillingForm :