Definition
Consider a Lie algebra g over a field K. Every element x of g defines the adjoint endomorphism ad(x) (also written as adx) of g with the help of the Lie bracket, as
- ad(x)(y) = .
Now, supposing g is of finite dimension, the trace of the composition of two such endomorphisms defines a symmetric bilinear form
- B(x, y) = trace(ad(x)ad(y)),
with values in K, the Killing form on g.
Read more about this topic: Killing Form
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